Answer:
A. There is sufficient evidence to prove and conclude that the true average percentage differs from desired percentage.
B. P(Z<-4.93333) = 0.0000
C. n = 5945 samples
Step-by-step explanation:
A)
The rightnull and alternative hypotheses are given as below:
Null hypothesis H0: µ = 5.5
Alternative hypothesis Ha: µ ≠ 5.5
Conducting the one sample z test for population mean.
Test statistic formula is given as below:
Z = (Xbar - µ)/[σ/√(n)]
Given,
Xbar = 5.23
µ = 5.5
σ = 0.30
n = 16
Z = (5.23 – 5.5) / [ 0.30 /√(16)]
Z = -3.6000
P-value = 0.0003
α value = 0.05
P-value < α value
So, we reject the null hypothesis. There is sufficient evidence to prove and conclude that the true average percentage differs from desired percentage.
B
From the information given
Xbar = 5.23
µ = 5.6
σ = 0.30
n = 16
α value = 0.01
Z = (Xbar - µ)/[σ/√(n)]
Z = (5.23 - 5.6)/(0.30/√(16))
Z = -4.93333
P(Z<-4.93333) = 0.0000
Required probability = 0.0000
C
We are given α =0.01
Therefore, critical Z value = 2.57
E = 0.01
σ = 0.30
n = (Z*σ/E)^2
n = (2.57*0.30/0.01)^2 = 5944.41
n = 5945 samples
A labourer is paid #1000 for5 days work. what is his pay for 22days work
Final answer:
To calculate the labourer's pay for 22 days, divide the total pay for 5 days by 5 to get the daily wage, and then multiply this by 22. The labourer would earn #4400 for 22 days of work.
Explanation:
The question posed is regarding the calculation of a laborer's pay for a certain number of days based on a known daily wage rate.
If a labourer is paid #1000 for 5 days work, to find out his pay for 22 days work we follow these steps:
Firstly, we calculate the daily wage by dividing the total pay by the number of days worked. That is, #1000 / 5 days = #200 per day.Next, we multiply the daily wage by the number of days in question to get the total pay for that period. So for 22 days: #200 per day * 22 days = #4400.In conclusion, the labourer's pay for 22 days of work would be #4400.
In recent years, the IRS has been inundated with taxpayer calls and has redesigned its phone service as well as posting answers to frequently asked questions on its website (The Cincinnati Enquirer, January 7, 2010). According to a report by a taxpayer advocate, callers using the new system can expect to wait on hold for an unreasonably long time of minutes before being able to talk to an IRS employee. Suppose you select a sample of callers after the new phone service has been implemented; the sample results show a mean waiting time of minutes before an IRS employee comes on line. Based upon data from past years, you decide is it reasonable to assume that the standard deviation of waiting times is minutes 11?
Answer:
The calculated p-value is greater than the significance level at which the test was performed, hence, we fail to reject the null hypothesis & conclude that there is no significant evidence to say that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate.
That is, the true mean waiting time is equal to or greater than the 15-minute claim by the taxpayer advocate.
Step-by-step explanation:
For hypothesis testing, we first clearly state our null and alternative hypothesis.
For hypothesis testing, the first thing to define is the null and alternative hypothesis.
In hypothesis testing, especially one comparing two sets of data, the null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the direction of the test.
The alternative hypothesis usually confirms the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the direction of the test.
For this question, we are to investigate that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate.
The null hypothesis would be that there is no significant evidence to say that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate. That is, the true mean waiting time is equal to or greater than the 15-minute claim by the taxpayer advocate.
The alternative hypothesis is that there is significant evidence to suggest that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate.
This is evidently a one tail hypothesis test (we're investigating only in one direction; less than the claim
Mathematically, the null hypothesis is
H₀: μ ≥ 15
The alternative hypothesis is
Hₐ: μ < 15 minutes
To do this test, we will use the z-distribution because the population standard deviation is known.
So, we compute the z-test statistic
z = (x - μ₀)/σₓ
x = sample mean = 13 minutes
μ₀ = the advocate's claim = 15 minutes
σₓ = standard error of the poll proportion = (σ/√n)
where n = Sample size = 50
σ = population standard deviation = 11 minutes.
σₓ = (σ/√n) = (11/√50) = 1.556
z = (13 - 15) ÷ 1.556 = -1.29
checking the tables for the p-value of this z-statistic
p-value (for z = -1.29, at 0.05 significance level, with a one tailed condition) = 0.098525
The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 5% = 0.05
p-value = 0.098525
0.098525 > 0.05
Hence,
p-value > significance level
This means that we fail to reject the null hypothesis & conclude that there is no significant evidence to say that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate.
That is, the true mean waiting time is equal to or greater than the 15-minute claim by the taxpayer advocate.
Hope this Helps!!!
An expression equal to 8x + 24
Answer:
8 ( x + 3 ) , Need more details , hope this was answer
Step-by-step explanation:
Final answer:
The expression 8x + 24 can be factored to 8(x + 3) by taking out the common factor of 8, which is a usual step in simplifying algebraic expressions.
Explanation:
The expression 8x + 24 is a linear algebraic expression with two terms. Typically in algebra, when simplifying expressions or solving equations, we might look for ways to factor or combine like terms. However, in this expression, there's no immediate algebraic simplification other than factoring out a common factor if we wanted to rewrite the expression in a different form.
If we observe that 24 is divisible by 8, we might factor out the number 8 to express the original expression in the form of 8(x + 3). This shows that the expression can be seen as the product of 8 and the quantity (x + 3), which is particularly useful when solving equations or simplifying further expressions that include 8x + 24.
Please help with this math question
Answer:
Im not 100% sure but i think its first row second
Answer: all the triangle are similar
Step-by-step explanation: ;)
Morgan can make 4 cupcakes (the y value) with one cup of flour (the x value). How many cupcakes can she make with 18 cups of flour?
Answer:
y = 18x
72 cupcakes = 18 cups of flour
Step-by-step explanation:
y= cupcakes
x=flour
4/1
72/18
18x4=72
Answer:
72 cupcakes
Step-by-step explanation:
Take 4 and multiply it by 18! Simple! :)
In circle T, ZPTQ E ZRTS.
What is the length of PQ?
3 units
4 units
6 units
7 units
Since PQ = SR, hence the length of PQ is 4 units
Similar shapesFrom the given figure, w are told that triangle PTQ is similar to that of RTS, this means that;
PQ = SR
Given the following
Length of SR = 4 units
Since PQ = SR, hence the length of PQ is 4 units
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If you were to create a histogram from the data shown in the stem-and-leaf plot, with each bar covering six values from 13 to 42, how many data points would be in the bar from 13 - 18?
Answer:
4
Step-by-step explanation:
4 data points are between 13 and 18 they are 13, 14, 15, and 18.
Answer:
4
Step-by-step explanation:
i took test
A researcher is interested in seeing if negative political ads against an opponent (group one) are more effective than positive ads for the original candidate (group two). If the mean for group one is 7.00, the mean for group two is 10.00, the n for group one is 20, the n for group two is 20, the variance for group one is 2.50, and the variance for group two is 4.5.
What is the correct write up for this study in a results section?A. t(40) = 5.07, p < .01B. t(38) = .592, p > .05C. t(19) = 5.07, p < .01D. t(38) = 2.59, p > .05E. None of the above (it should be t(38) = 5.07, p < .01)
Answer:
[tex]t=\frac{10-7}{\sqrt{\frac{1.581^2}{20}+\frac{2.121^2}{20}}}}=5.07[/tex]
The first step is calculate the degrees of freedom, on this case:
[tex]df=n_{1}+n_{2}-2=20+20-2=38[/tex]
Since is a one side test the p value would be:
[tex]p_v =P(t_{(38)}>5.07)=5.33x10^{-6}[/tex]
And the best option for this case would be:
None of the above (it should be t(38) = 5.07, p < .01)
Step-by-step explanation:
Data given and notation
[tex]\bar X_{1}=7[/tex] represent the mean for the sample 1
[tex]\bar X_{2}=10[/tex] represent the mean for the sample 2
[tex]s_{1}=\sqrt{2.5}= 1.581[/tex] represent the sample standard deviation for the sample 1
[tex]s_{2}=\sqrt{4.5}= 2.121[/tex] represent the sample standard deviation for the sample 2
[tex]n_{1}=20[/tex] sample size selected for 1
[tex]n_{2}=20[/tex] sample size selected for 2
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean for the group 1 is higher than the mean for group 2, the system of hypothesis would be:
Null hypothesis:[tex]\mu_{2} \leq \mu_{1}[/tex]
Alternative hypothesis:[tex]\mu_{2} > \mu_{1}[/tex]
If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:
[tex]t=\frac{\bar X_{2}-\bar X_{1}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{10-7}{\sqrt{\frac{1.581^2}{20}+\frac{2.121^2}{20}}}}=5.07[/tex]
P-value
The first step is calculate the degrees of freedom, on this case:
[tex]df=n_{1}+n_{2}-2=20+20-2=38[/tex]
Since is a one side test the p value would be:
[tex]p_v =P(t_{(38)}>5.07)=5.33x10^{-6}[/tex]
And the best option for this case would be:
None of the above (it should be t(38) = 5.07, p < .01)
The product of two given numbers is 126 both of them are divisible by 3 but neither of them is 3.The larger of the two numbers is
I believe the answer is 21
21 × 6 = 126
and both numbers are divisible by 3
Roger has 4 gallons of juice. He puts the same amount of juice into each of 5 pitchers. How many gallons of juice are in 1 pitcher?
Answer:
0.8 gallons
Step-by-step explanation:
4 gallons of juice divided into 5 pitchers equally, 4/5=0.8 per pitcher.
How do you get the answer to 54-200 divide by 4
Answer:
4
Step-by-step explanation:
use the order of operations- (parentheses, exponets, multiply, divide, add, subtract...)
54-200/4
-200/4=-50
54-50=4
7. Certain car manufacturers install a gauge that tells the driver how many miles they can drive
until they will run out of gas. A study was conducted to test the accuracy of these gauges.
Each driver was assigned a certain gauge reading until empty to watch for. When their car
announced it had that many miles remaining until empty, they began to measure their
distance traveled. After they ran out of gas, they reported the distance they were able to dove
(in miles) as well as the gauge reading they were assigned (in miles). Here is computer output
showing the regression analysis:
Regression Analysis: Distance versus Gauge Reading
Predictor Coef SE Coef
Constant -0.7928 3.2114
-0.2469 0.8060
Gauge 1.1889 0.0457
26.0310 0.0000
5 - 7.0032
R-Sq -0.9326 R-Sqladj) - 0.9312
Identify and interpret the slope of the regression line used for predicting the actual distance
that can be driven based on the gauge reading
(A) Slope - 1.1889. The predicted distance the drivers were able to drive increases by 1.1889
miles for each additional mile reported by the gauge.
(B) Slope - 0.0457. The predicted distance the drivers were able to drive increases by 0.0457
miles for each additional mile reported by the gauge.
(C) Slope - -0.7928. The predicted distance the drivers were able to drive decreases by
0.7928 miles for each additional mile reported by the gauge.
(D) Slope - 1.1889. For each additional mile reported by the gauge, the drivers were able to
drive an additional 1.1889 miles
(E) Slope -0.0457. For each additional mile reported by the gauge, the drivers were able to
drive an additional 0.0457 miles,
Answer:
A) Slope - 1.1889. The Predicted distance the drivers were able to drive increases by 1.1889
Step-by-step explanation:
Find the margin of error for a 95% confidence interval for estimating the population mean when the sample standard deviation equals 100, with a sample size of (i) 484 and (ii) 1521. What is the effect of the sample size? (i) Find the margin of error for a 95% confidence interval for estimating the population mean when the sample standard deviation equals 100 with a sample size of 484.
Answer:
i) the margin of error for a 95% confidence interval for estimating the population mean is
M.E = 8.909
ii) the margin of error for a 95% confidence interval for estimating the population mean is
M.E = 5.025
Step-by-step explanation:
Step:-(i)
i ) Given sample size n = 484
Given sample standard deviation 'S' = 100
Margin of error for 95% confidence interval for estimating the population mean is determined by
[tex]M.E = \frac{1.96 X 100}{\sqrt{484} } = 8.909[/tex]
ii) Given sample size n =1521
Given sample standard deviation 'S' = 100
Margin of error for 95% confidence interval for estimating the population mean is determined by
[tex]M.E = \frac{1.96 X 100}{\sqrt{1521} } = 5.025[/tex]
People's Software Company has just set up a call center to provide technical assistance on its new software package. Two technical representatives are taking the calls, where the time required by either representative to answer a customer's questions has an exponential distribution with a mean of 5 minutes. Calls are arriving according to a Poisson process at a mean rate of 10 per hour. By next year, the mean arrival rate of calls is expected to decline to 5 per hour, so the plan is to reduce the number of technical representatives to one then. a-) Assuming that service rate μ will stay the same for next year's queueing system, determine L, Lq, W, and Wq for both the current system and next year's system. For each of these four measures of performance, which system yields the smaller value? b-) Now assume that μ will be adjustable when the number of technical representatives is reduced to one. Solve algebraically for the value of μ that would yield the same value of W as for the current system.
The question revolves around calculating queueing system performance measures for a software company's call center and adjusting the service rate to maintain consistent service levels during an operational change. Calculations would apply queue theory but specifics require further details about the model type, such as M/M/1 or M/M/2. Algebraic methods would be needed to adjust the service rate to keep waiting times consistent.
Explanation:The question deals with determining key performance measures (L, Lq, W, Wq) for a queueing system at People's Software Company call center, under two different operational scenarios, and solving for the service rate (μ) that equates waiting times between these scenarios. The system initially with two representatives and an arrival rate of 10 calls per hour, transitioning to one representative and a decreased arrival rate of 5 calls per hour, is examined assuming exponential service times with a mean of 5 minutes.
For the current system with two technical representatives and ten calls arriving per hour, assuming the call arrival rate follows a Poisson process and service times are exponentially distributed, key performance measures could be calculated utilizing formulas from queueing theory. However, these formulas depend highly on the specifics of the queueing model used, such as M/M/1, M/M/2, etc., and are not directly provided here.
For next year's system with a reduction in technical representatives and a halved arrival rate, similar analytical methods could be applied to predict performance based on the adjusted arrival rate and the assumption of unchanged service time distributions.
Regarding the adjustment of μ to maintain the same waiting time (W), algebraic solutions involving the exponential service time distribution and Poisson arrival processes must be derived, factoring in the reduction of workers and the change in arrival rate, to find the new service rate (μ) that would ensure continuity in service level expectations.
What is the distance between –5 and 2?
units
Answer:
it would be a distance of 7 units
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
the absolute value of -5 - 2 = 7
(1.64x10^0)/(2.0x10^2) answers in scientific notation
Answer:
8.2*10^-3
Step-by-step explanation:
Answer:
0.0082
(scientific notation)-step explanation:
Find the minimum sample size when we want to construct a 90% confidence interval on the population proportion for the support of candidate A in the following mayoral election. Candidate A is facing two opposing candidates. In a preselected poll of 100 residents, 22 supported her. The desired margin of error is 0.08.
Having issues solving
Answer:
Step-by-step explanation:
Labor: 40.55 x 4 = $162.20 for total Labor.
Total Charges: 25.75 + 38.75 + 162.20 = $226.70 Total charges.
Circle P has a circumference of approximately 75 inches.
What is the approximate length of the radius, m? Use 3.14 for
TT. Round to the nearest inch,
O 12 inches
O 24 inches
O 38 inches
46 inches
Answer: 12
Step-by-step explanation: To find the radius you have to do the opposite of 2r(pi). So you divide 75 by 2 and then by 3.14, getting 11.9, which rounds to 12
Answer:
1) 12in
Step-by-step explanation:
The circumference is 75, so to find the diameter you have to divide 75 by 3.14. You get 24 approximately. Then divide the diameter by 2, so 24/2=12.
According to a "how to stop bullying" Web site, 15% of students report experiencing bullying one to three times within the most recent month. Let's assume the standard deviation is 4.5% of students. Joseph collects data from 186 students at a medium-sized school in Iowa and finds that only 11% reported this rate of bullying. What is his 95% confidence interval?
Using the formula for a 95% confidence interval and a Z score of 1.96, Joseph's 95% confidence interval for the percentage of students reporting bullying at their school is roughly 10.1% to 11.9%.
Explanation:The subject of this problem is statistics, specifically the creation of a 95% confidence interval based on collected data. A confidence interval is a type of estimate computed from the statistics of observed data. This gives a range of values for an unknown parameter (in this case, the number of students experiencing bullying).
In this case, the mean (or average) is 0.15 or 15%. The standard deviation is 0.045 or 4.5%. The sample size, often denoted as 'n', is 186.
Based on the 95% confidence interval, we will use a Z score of 1.96. We can start to calculate our interval using the formula for the confidence interval: sample mean ± (Z * (standard deviation/sqrt(n))).
Using these numbers:
The lower end of the confidence interval is 0.11 - (1.96 * (0.045 / sqrt(186))) = about 0.101 or 10.1%.
The upper end of the confidence interval is 0.11 + (1.96 * (0.045 / sqrt(186))) = about 0.119 or 11.9%.
So, the 95% confidence interval for the percentage of students who reported experiencing bullying one to three times within the most recent month is approximately 10.1% to 11.9%.
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what is -3 3/4 + 1/2
Answer: -3 1/4 or -13/4
Step-by-step explanation:
Answer:
[tex]\frac{-7}{4}[/tex]
Step-by-step explanation:
-3*3/4-1/2
-9/4+1/2
-9/4+2/4
(-9+2)/4
-7/4
2y2(35 – 4y) in standard form
Step-by-step explanation:
[tex]2 {y}^{2} (35 - 4y) \\ = 2 {y}^{2} \times 35 - 2 {y}^{2} \times 4y \\ = 70 {y}^{2} - 8 {y}^{3} \\ = \red { \bold{ - 8 {y}^{3} + 70 {y}^{2} }} \\ is \: in \: the \: standard \: form.[/tex]
What is the midpoint of AC ?
A: (m + p, n + r)
B: (p – m, r – n)
C: (m – p, n – r)
D: (m + n, p + r)
Answer:
A: (m + p, n + r)
Step-by-step explanation:
[tex]Midpoint \: of \: AC \\ = \bigg( \frac{2m + 2p}{2} \: \: \frac{2n + 2r}{2} \bigg) \\ \\ = \bigg( m + p, \: \: n + r \bigg)[/tex]
A box is to be made where the material for the sides and the lid cost $0.20 per square foot and the cost for the bottom is $0.650.65 per square foot. Find the dimensions of a box with volume 1010 cubic feet that has minimum cost.
Answer:
the dimensions xyz of a box with volume 10 cubic feet that has minimum cost is;
x = 1.68 ft
y = 1.68 ft
z = 3.54 ft
Step-by-step explanation:
See attachment for the full explanation.
a car was valued at $41,000 in the year 2009 by 2013 the car value has depreciated to 19,000 if the car value continues to by the same percentage what will it be worth in 2019?
Answer:
$6,376.92
Step-by-step explanation:
-Let d be the rate of depreciation per year.
-Therefore, the value after n years can be expressed as:
[tex]A=P(1-d)^n\\\\A=Value \ after \ n \ years\\P=Initial \ Value\\d=Rate \ of \ depreciation\\n=Time \ in \ years[/tex]
#We substitute for the years 2009-2013 to solve for d:
[tex]A=P(1-d)^n\\\\19000=41000(1-d)^4\\\\0.475=(1-d)^4\\\\d=1-0.475^{0.25}\\\\d=0.1698[/tex]
#We then use the calculated depreciation rate above to solve for A after 10 yrs:
[tex]A=P(1-d)^n\\\\=41000(1-0.1698)^{10}\\\\=\$6,376.92[/tex]
Hence, the value of the car after 10 yrs is $6,376.92
To find the future value of a car in 2019, we calculate the percentage decrease in value from 2009 to 2013 and apply it for 6 years.
Explanation:To find the future value of the car in 2019, we need to determine the percentage decrease in value each year. From 2009 to 2013, the car depreciated from $41,000 to $19,000.
This is a decrease of $22,000. To find the percentage decrease, divide this by the initial value: 22,000 / 41,000 = 0.5366 (approximately).
To find the future value in 2019, we need to apply this percentage decrease continuously for 6 years. Multiply the current value by the percentage decrease repeatedly.
= 19,000 * 0.5366 * 0.5366 * 0.5366 * 0.5366 * 0.5366 * 0.5366
= $5,862.54 (approximately).
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A triangle has a base of 4 m and a height of 3 m. Find the area of the triangle in square millimeters.
Answer:
6000000 mm squared
Step-by-step explanation:
We first convert the meters to millimeters. We got 4000 and 3000. The area of a triangle is base times height divided by 2. So we get 12000000 divided by 2 or 6000000 mm squared
Jenny has a toy which is in the shape of a right prism with triangular bases. The sides of its bases are each 5 feet and its approximate height is 4.3 feet. The length of the prism between the bases is 12 feet. What is the approximate surface area of this right prism?
A. 150ft2 B. 201.5ft2
C.210ft2 D.225.4ft2
Answer:
B
Step-by-step explanation:
split the triangle in to 5 different shapes
3 of them are rectangles, and 2 are triangles
all of the rectangles are the same size being:
12 by 5 so 12 times 5. then do this 3 times for each rectangle.
Now take the triangles and find the area for those.
which is 1/2 or base times height . so half of 5 multiplied by height (4.3)
being 2.5 times 4.3 giving you 10.75
now take the area of the rectangles and triangles and add them together
60+60+60+10.75+10.75= 201.5 ft2
Solve 2/5 (j + 40) = -4 *
Answer: j=-5 as long as you follow my steps you will also be able to show your work.
Combine multiplied terms into a single fraction
Distribute it then
Multiply all terms by the same value to eliminate fraction denominators.
A manufacturing plant earned $80 per man-hour of labor when it opened. Each year, the plant earns an additional 5% per man-hour.
Answer:
if you divide 80 and 5 would give you 16
Step-by-step explanation:
Find the unit rate for the situation: Corrin has twin boys. She buys a box ot
10 toy cars to share evenly between the boys. *
(1) Given:
Given that Corrin has twin boys. She buys a box of 10 toy cars to share evenly between them.
We need to determine the unit rate of toy cars for one boy.
Unit rate:
The unit rate for toy cars for one boy can be determined by dividing the total number of cars by the total number of boys.
Thus, we have;
[tex]Unit \ rate=\frac{10}{2}[/tex]
[tex]Unit \ rate=5[/tex]
Thus, the unit rate is 5 cars per boy.
Hence, Option b is the correct answer.
(2) Given:
Given that the Belle works at a donut shop. They sell a box of donut holes for $1.80. There are 20 donut holes in the box.
We need to determine the unit rate.
Unit rate:
We need to determine the cost of one donut hole in the box.
The cost of one donut hole can be determined by dividing the cost of box of donut holes by the total number of donut holes in the box.
Thus, we have;
[tex]Unit \ rate=\frac{1.80}{20}[/tex]
[tex]Unit \ rate=0.09[/tex]
Thus, the unit rate is $0.09 per donut hole.
Hence, Option a is the correct answer.