Suppose µX and µY are the true mean stopping distances when starting at 50 mph for cars of a
certain type equipped with two different braking systems (System X vs. System Y). The
following data was obtained for each braking system:

System X    System Y
nx = 8           ny = 8
x = 85.7 ft    y = 96.3 ft
sx = 4.36 ft sy = 5.18 ft
Consider the following hypotheses:
Ho: µX - µY = -5
Ha: µX - µY < -5
As indicated by the alternative hypothesis, it is believed that cars equipped with System X
are able to stop over a shorter distance than cars equipped with System Y. Does the data
support this hypothesis at the 1% level?

Identify the advantages and disadvantages of monetary-unit sampling.

The advantages include that monetary-unit-sampling will result in a smaller sample size than classical variable sampling. It also results in a stratified sample item when samples are selected using MUS. The results of the calculation of sample size and the evaluation of the sample aren't based on the standard deviation. The disadvantages include the overstatement of the allowance of sampling risk if MUS is used to detect misstatements. Special design consideration is required using a selection of zero or negative balances. The sample error is assumed to be no more than 100%.

Can you expound further on this? Thanks!

Construct the confidence interval for the population mean

muμ.

cequals=0.980.98 ,

x overbar equals 9.1x=9.1 ,

sigmaσequals=0.40.4 ,

and

nequals=4141

A 9898 % confidence interval for muμ is (___,___) (Round to two decimal places as needed.)

Kaneko has two groups. She randomly assigns subjects to her two groups. She has one group read a news article about the importance of a public speaking classes to one’s ability to get a job, while the other group reads a news article about a recent college football game that took place at her university. Then she asks both groups to rate how important they believe a public speaking class is to one’s ability to get a job(0-50). She thinks the groups will be different but does not make a specific prediction about the direction of the difference. She wants to use α = .01. Public SpeakingGroupFootball GroupMean4530s64n4035a.What test should Kaneko use?b.Write out Kaneko’s null and alternative hypotheses in formula form.c.What is the calculated value?d.What is the critical value using α = .01?e.Make a statistical and substantive conclusion for the above problem.f. Calculate eta-square and omega-square for this problem. Interpret what these numbers mean.

The ideal (daytime) noise-level for hospitals is 45 decibels with a standard deviation of 12 db; which is to say, this may not be true. A simple random sample of 75 hospitals at a moment during the day gives a mean noise level of 47 db. Assume that the standard deviation of noise level for all hospitals is really 12 db. All answers to two places after the decimal.
(a) A 99% confidence interval for the actual mean noise level in hospitals is   db,   db).

(b) We can be 90% confident that the actual mean noise level in hospitals is   db with a margin of error of db.

(c) Unless our sample (of 81 hospitals) is among the most unusual 2% of samples, the actual mean noise level in hospitals is between db and   db.

(d) A 99.9% confidence interval for the actual mean noise level in hospitals is   db,    db).

(e) Assuming our sample of hospitals is among the most typical half of such samples, the actual mean noise level in hospitals is between   db and   db.

(f) We are 95% confident that the actual mean noise level in hospitals is db, with a margin of error of db.

(g) How many hospitals must we examine to have 95% confidence that we have the margin of error to within 0.5 db?  

(h) How many hospitals must we examine to have 99.9% confidence that we have the margin of error to within 0.5 db?

I am having trouble differentiating these. Can someone provide steps for these? I only need 1-3, 4 is always rejecting or failing to reject null.

- Hypothesis testing (4 steps) for comparing variances when sample sizes are equal.

- Hypothesis testing (4 steps) for comparing variances when sample sizes are not equal.

- Hypothesis testing (4 steps) with the independent-measures t statistic (variances assumed unequal). Be able to compute effect size using r^2.

Thank you :)

According to the National Automobile Dealers Assoc., 75% of U.S. car dealers' profits comes from repairs and parts sold. However, many of the dealerships' service departments aren't open evenings or weekends. The percentage of dealerships opened during the evenings and weekends are as follows:

Suppose a random sample of size 59 is selected from a population with σ = 10. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).

a. The population size is infinite (to 2 decimals).

b. The population size is N = 50,000 (to 2 decimals).

c. The population size is N = 5000 (to 2 decimals).

d. The population size is N = 500 (to 2 decimals).

Two plots at Rothamsted Experimental Station were studied for production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows.

Use a calculator to verify that, for this plot, the sample variance is s² ≈ 0.294.

Another random sample of years for a second plot gave the following annual wheat production (in pounds).

Use a calculator to verify that the sample variance for this plot is s² ≈ 0.959.

Test the claim that there is a difference (either way) in the population variance of wheat straw production for these two plots. Use a 5% level of signifcance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: σ₁² = σ₂²; H₁: σ₁² > σ₂²H_o: σ₁² > σ₂²; H₁: σ₁² = σ₂²    H_o: σ₂² = σ₁²; H₁: σ₂² > σ₁²H_o: σ₁² = σ₂²; H₁: σ₁² ≠ σ₂²

(b) Find the value of the sample F statistic. (Use 2 decimal places.)


What are the degrees of freedom?

What assumptions are you making about the original distribution?

The populations follow independent chi-square distributions. We have random samples from each population.The populations follow independent normal distributions. We have random samples from each population.    The populations follow independent normal distributions.The populations follow dependent normal distributions. We have random samples from each population.

(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)

p-value > 0.2000.100 < p-value < 0.200    0.050 < p-value < 0.1000.020 < p-value < 0.0500.002 < p-value < 0.020p-value < 0.002

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.    At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.Reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.    Reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.Fail to reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.

Question 14 Consider the following sample of 11 length-of-stay values (measured in days): 1, 1, 3, 3, 3, 4, 4, 4, 4, 5, 7 Now suppose that due to new technology you are able to reduce the length of stay at your hospital to a fraction 0.5 of the original values. Thus, your new sample is given by .5, .5, 1.5, 1.5, 1.5, 2, 2, 2, 2, 2.5, 3.5 Given that the standard deviation in the original sample was 1.7, in the new sample the standard deviation is _._. (Truncate after the first decimal.)

A furniture store has maintained monthly sales records for the past 20​ months, with the results shown below.

Assume you have determined there is NO SEASONALITY in this time series.​ Therefore, you want to fit a linear trend model​ (that is, trend​ only) to the data.

Calculate the linear trend equation.​ (Round coefficients to the nearest whole​ number.)

y= _+ _ * t

nothing​*t

What are the test statistic and​ p-value to test for a significant trend. Round both to two decimal places.

T​ =

​p-value =

Is the trend significant using a​ 10% significance​ level?

Yes

No

What is the value of​ R-squared? (Round to two​ decimals.)

Forecast the sales for the next month​ (t =​ 21). (Round to the nearest whole​ number.)

Upper F21=?

Based on the​ R-squared value, how confident are you in this​ forecast? (That​ is, how accurate do you think the forecasts will​ be?)

A.

Not confident at all because the​ R-squared value is so low

B.

Very confident because the​ R-squared value is high

C.

Somewhat confident because the​ R-squared value is moderate​ (not extremely high but not extemely​ low)

Click to select your answer(s).

A particular report included the following table classifying 712 fatal bicycle accidents according to time of day the accident occurred.

(a) Assume it is reasonable to regard the 712 bicycle accidents summarized in the table as a random sample of fatal bicycle accidents in that year. Do these data support the hypothesis that fatal bicycle accidents are not equally likely to occur in each of the 3-hour time periods used to construct the table? Test the relevant hypotheses using a significance level of .05. (Round your χ² value to two decimal places, and round your P-value to three decimal places.)

What can you conclude?

There is sufficient evidence to reject H₀. There is insufficient evidence to reject H₀.    

(b) Suppose a safety office proposes that bicycle fatalities are twice as likely to occur between noon and midnight as during midnight to noon and suggests the following hypothesis: H₀: p₁ = 1/3, p₂ = 2/3, where p₁ is the proportion of accidents occurring between midnight and noon and p₂ is the proportion occurring between noon and midnight. Do the given data provide evidence against this hypothesis, or are the data consistent with it? Justify your answer with an appropriate test. (Hint: Use the data to construct a one-way table with just two time categories. Use α = 0.05. Round your χ² value to two decimal places, and round your P-value to three decimal places.)

What can you conclude?

There is sufficient evidence to reject H₀. There is insufficient evidence to reject H₀.    

You may need to use the appropriate table in Appendix A to answer this question.

ou are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals.

A random sample of

3939

gas grills has a mean price of

$632.10632.10.

Assume the population standard deviation is

$55.6055.60.

The 90% confidence interval is (____,___)

Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm) (BBC News website). Assume that the height of men in the Netherlands is normally distributed with a mean of 183 cm and standard deviation of 10.5 cm.

a.What is the probability that a Dutch male is shorter than 175 cm?

b.What is the probability that a Dutch male is taller than 195 cm?

c.What is the probability that a Dutch male is between 173 and 193 cm?

d.Out of a random sample of 1000 Dutch men, how many would we expect to be taller than 190 cm?