Construct a 95 confidence interval for u1 u2

1. A recent study found that children who watched a cartoon with food advertising​ ate, on​ average,

27.327.3 grams of crackers as compared to an average of 21.321.3 grams of crackers for children who watched a cartoon without food advertising. Suppose that there were 5858 children in each​ group, and the sample standard deviation for those children who watched the food ad was 8.38.3 grams and the sample standard deviation for those children who did not watch the food ad was

8.18.1 grams. Complete parts​ (a) and​ (b) below.

A. What is the test​ statistic?

B. What is the correct​ conclusion?

C. Assuming that the population variances are​ equal, construct a 95​% confidence interval estimate of the difference u1-u2 between the mean amount of crackers eaten by the children who watch and do not watch the food ad.

2. A bank with branches located in a commercial district of a city and in a residential district has the business objective of developing an improved process for serving customers during the​ noon-to-1 P.M. lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the time that elapses from when the customer enters the line until he or she reaches the teller window. Data are collected from a random sample of 15 customers at each branch. Complete​ (a) through​ (d) below.

Assuming that the population variances from both banks are not​ equal, is there evidence of a difference in the mean waiting time between the two​ branches? (Use

Alpha αequals=0.05) Determine the hypotheses. Let μ1 be the mean waiting time of the commercial district branch and μ2 be the mean waiting time of the residential district branch. Choose the correct answer below.

Determine the test statistic.

Determine the critical​ value(s).

Choose the correct conclusion below. Reject or not reject with sufficient or insufficient evidence

In addition to unequal​ variances, what assumption is necessary in​ (a)?Choose the correct answer below

A. Since the sample sizes are both less than​ 30, it must be assumed that the sample sizes are equal.

B. Since the sample sizes are both less than​ 30, it must be assumed that the samples are specifically chosen and not independently sampled.

C. Since the sample sizes are both less than​ 30, it must be assumed that the sample variances are equal.

D. Since the sample sizes are both less than​ 30, it must be assumed that both sampled populations are approximately normal.

3. Construct and interpret a 95​% confidence interval estimate of the difference between the population means in the two branches.

4. Which of the following is the best interpretation of the confidence​ interval?Choose the best answer.

A. One can conclude with 95​% confidence that the difference between the sample mean wait times of the two branches falls inside this interval.

B. One can conclude with 95​% confidence that the difference between the sample mean wait times of the two branches falls outside this interval.

C. One can conclude with 95​% confidence that the difference between the population mean wait times of the two branches falls inside this interval.

D. One can conclude with 95​% confidence that the difference between the population mean wait times of the two branches falls outside this interval.

5. . Assuming equal variances between the two populations yields a t stat test statistic of -4.0758. How do these results compare to the results found in​ (a)?Choose the correct answer

A. Observing a difference this large or larger in the two sample means is less likely if you assume equal population variances than if you assume unequal​ variances, but the null hypothesis would be rejected either way.

B. Assuming equal population variances results in the same tstat test​ statistic, which means that whether or not the variances are equal will not have any affect on the tstat test statistic under any circumstance.

5. An evaluation was recently performed on brands and data were collected that classified each brand as being in the technology or financial institutions sector and also reported the brand value. The results in terms of value​ (in millions of​ dollars) are shown in the accompanying data table. Complete parts​ (a) through​ (c).

Determine the hypotheses. Let μ1 be the mean brand value for the technology sector and μ2

be the mean brand value for the financial institutions sector. Choose the correct answer below.

B. Find the test statistic

C. Reject or don’t reject with insufficient or sufficient evidence to support

D. Repeat​ (a), assuming that the population variances are not equal.Determine the hypotheses.

E. Find the test statistic.

F.Reject or do not reject H0 sufficient evidence or insufficient evidence to support?

G. Compare the results of​ (a) and​ (b).Choose the correct answer.

A. The conclusions for parts​ (a) and​ (b) both reject the null hypothesis.

B. The conclusions for parts​ (a) and​ (b) are different. Reject the null hypothesis in​ (a) and do not reject it in​ (b).

C. The conclusions for parts​ (a) and​ (b) are different. Reject the null hypothesis in​ (b) and do not reject it in​ (a).

D. The conclusions for parts​ (a) and​ (b) both do not reject the null hypothesis.

6. n intaglio​ printing, a design or figure is carved beneath the surface of hard metal or stone. The business objective of an intaglio printing company is to determine whether there are differences in the mean surface hardness of steel​ plates, based on two different surface conditionslong dash—untreated and treated by lightly polishing with emery paper. An experiment is designed in which 40 steel plates are randomly assigned long dash—20 plates are treated and 20 plates are untreated. The results can be found by clicking the icon. Complete​ (a) through​(d) below.

Assuming the population variances from both conditions are​ unequal, is there evidence of a difference in the mean surface hardness between untreated and treated steel​plates? (Use

alpha equals 0.05α=0.05​.)Determine the hypotheses. Let μ1 be the mean surface hardness of the treated plates and μ2 be the mean surface hardness of the untreated plates. Choose the correct answer below.

B. what is the test statistic

C. what is/are the critical values