# 10 statistics problems dealing with hypothesis testing

(The table is the student's t values generated by Minitab Version 9.2. Do not show sketches)

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Statistics Problems#1

Marketing: Shopping Time - How much customers buy is a direct result of how much time they spend in the store. A study of average shopping time in a large national house ware store gave the following information

Women with female companion: 8.3 minutes

Women with male companion: 4.5 minutes

Suppose you want to set up a statistical test to challenge the claim that a woman with a female friend spends an average of 8.3 minutes shopping in such a store.

A. What would you use for the null and alternate hypotheses if you believe the average shopping time is less than 8.3 minutes? Is the critical region on the right, on the left , or on both sides of the mean?

B. What would you use for the null and alternate hypotheses if you believe the average shopping time is different from 8.3 minutes? Is the critical region on the right, on the left, or on both sides of the mean?

Stores that sell mainly to women should figure out a way to engage the interest of men! Perhaps comfortable seats and a big TV with sports programs. Suppose such an entertainment center was installed and now you wish to challenge the claim that a woman with a male friend spends only 4.5 minutes shopping in a house ware store.

C. What would you use for the null and alternate hypotheses if you believe the average shopping time is more than 4.5 minutes? Is the critical region on the right, on the left, or on both sides of the mean?

D. What would you use for the null and alternate hypotheses if you believe the average shopping time is different from 4.5 minutes? Is the critical region on the right, on the left, or on both sides?

Problem#2

Chrysler Concorde: Acceleration Consumer Reports stated that the mean time for a Chrysler Concorde to go from 0 to 60 miles per hour was 8.7 seconds.

A. If you want to set up a statistical test to challenge the clair of 8.7 seconds, what would you use the null hypothesis?

B. The town of Leadville, Colorado, has an elevation over 10,000 feet, Suppose that you wanted to test the claim that the average time to accelerate from 0 to 60 miles per hour is longer in Leadville (because of less oxygen). What would you use for the alternate hypothesis?

C. Suppose that you made an engine modification and you think the average time to accelerate fro 0 to 60 miles per hour is reduced. What would yu use for the alternate hypothesis?

D. For each of the tests in parts (b) and (c), would the critical region be on the left, right, or both sides of the mean? Explain your answer in each case.

Problem#3

For problems 3,4,and 5 please provide the requested information.

a. What is the null hypothesis? What is the alternate hypothesis? Will we use a left-tailed, right-tailed, or two tailed test: What is the level of significance?

b. What sampling distribution will we use? What is the critical valueZo(or critical values +over_Zo)?

c. Sketch the critical region and show the critical value (or critical values).

d. Calculate the z value corresponding to the sample statistic -over x and show its location on the sketch of part (c).

e. Based on your answers for parts (a) to (d), shall we reject or fail to reject (i.e., "accept") the null hypothesis at the given level of significance ox? Explain your conclusion in the context of the problem.

f. Are the data statistically significant?

Problem#3

Ford Taurus: Assembly Time---Let x be a random variable that represents assembly time for the Ford Taurus. The Wall Street Journal reported that the average assembly time for the Ford Taurus is Mean= 38 hours. A modification to the assembly procedure has been made. It is thought that the average assembly time may be reduced because of this modification. A random sample of 47 new Ford Taurus automobiles coming off the assembly line showed the average assembly time to be -overx=37.5 hours with sample standard deviation s=12. does this indicate that the average time has been reduced? Use 0.01 as the level of significance.

Problem#4

Fashion Design: Display Windows-Judy Povich is a fashion design artist who designs the display windows in front of a large clothing store in New York City. Electronic counters at the entrances total the number of people entering the store each business day. Before Judy was hired by the store, the mean number of people entering the store each day was 3218. However, since Judy has started working, it is thought that this number has increased. A random sample of 42 business days after Judy began work an average -over x=3392 people entering the store each day. The sample standard deviation was s=287. Does this indicate that the average number of people entering the store each day has increased? Use a 1% level of significance.

Problem#5

Major League Baseball: Salary-The average annual salary of major league baseball players is now $1789556.00(source: USA Today). Suppose this year a random sample of 35 major league players in Florida had an average annual salary of _overx=$1621726.00 with a sample deviation s=$591218.00. Use a 1% level significance to test the claim that the average salary for all Florida players is different from the national average.

Problem#6

In Problem #6 use Table 5 of the Appendix to find the critical value(s) To for the described test of the mean (small sample)

Sample size n=13, right-tailed test, level of significance 1%.

Problem#7

For this problem please provide the requested information. Use for roblem#7 and 8.

A. What is the null hypothesis? What is the alternate hypothesis? Will we use a left -tailed test or a right tailed test. What is the level of signifance?

B. What sampling distribution will we use? What is the critical value To(or critical values +over-To)?

C. Sketch the critical region and show the cirtical value (or critical values).

D. Calculate the t value corresponding to the sample statistic -overx and show its location on the sketch of part c.

E. Find the P value ( or interval containing the P value) for your test and explain what the P value means in this context.

F. Based on your answers for parts a to e, shall we reject or fail to reject (i.e., "accept") the null hypothesis based on the given level of significance? Explain your conclusion in the context of the problem.

Medical: Hemoglobin Count-Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal with population mean about 14 for healthy adult women. Suppose that a female patient has taken 12 laboratory blood tests during the past year. The HC data sent to the patients doctor were

19 23 15 21 18 16

14 20 19 16 18 21

A. Use a calculator with a sample mean and sample standard deviation keys to verify that -overx =18.33 and s=2.71.

B. Does the information indicate that the population average HC for this patient is higher than 14? Use as level of significance =0.01.

Problem#8

Ski Patrol: Avalanches Snow-Snow avalanches can be a real problem for travelers in western United States and Canada. A very common type of avalanche is called the slab avalanche. These have been studied extensively by David McClung, a professor of civil engineering at the University of British Columbia. Slab avalanches studied in Canada had a average thickness of mean=67 cm (Source: Avalanche handbook ,by D. McClung and Pl Schaerer). The ski patrol at Vail, Colorado, is studying slab avalanches in their region. A random sample of avalances in spring gave the following thickness (cm):

59 51 76 38 65 54 49 62

68 55 64 67 63 74 65 79

a, Use a calculator with mean and standard deviation keys to verify that -overx=61.8 cm and s=10.6 cm.

b. Assume the slab thickness has an approximately normal distribution. Use a 1% level of significance to test the claim that the mean slab thickness in the Vail region is different from that in Canada.

Problem#9

In a statistical test, we have a choice of a left-tailed critical region, right-tailed critical region, or two -tailed critical region. Is it the null hypothesis or the alternate hypothesis that determines which type of critical region is used? Explain your answer.

Problem#10

If we reject the null hypothesis, does this mean that we have proven it to be false beyond all doubt? Explain your answer.

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#### Solution Preview

Please see the attached files for a better formatted solution

Statistics Problems#1

Marketing: Shopping Time - How much customers buy is a direct result of how much time they spend in the store. A study of average shopping time in a large national house ware store gave the following information

Women with female companion: 8.3 minutes

Women with male companion: 4.5 minutes

Suppose you want to set up a statistical test to challenge the claim that a woman with a female friend spends an average of 8.3 minutes shopping in such a store.

A. What would you use for the null and alternate hypotheses if you believe the average shopping time is less than 8.3 minutes? Is the critical region on the right, on the left , or on both sides of the mean?

The critical region is on the left (one-tailed test)

B. What would you use for the null and alternate hypotheses if you believe the average shopping time is different from 8.3 minutes? Is the critical region on the right, on the left, or on both sides of the mean?

Critical region would be on both sides of the mean (Two-tailed test)

Stores that sell mainly to women should figure out a way to engage the interest of men! Perhaps comfortable seats and a big TV with sports programs. Suppose such an entertainment center was installed and now you wish to challenge the claim that a woman with a male friend spends only 4.5 minutes shopping in a house ware store.

C. What would you use for the null and alternate hypotheses if you believe the average shopping time is more than 4.5 minutes? Is the critical region on the right, on the left, or on both sides of the mean?

Critical region would be on the right of the mean

D. What would you use for the null and alternate hypotheses if you believe the average shopping time is different from 4.5 minutes? Is the critical region on the right, on the left, or on both sides?

Critical region would be on both sides of the mean (Two-tailed test)

Problem#2

Chrysler Concorde: Acceleration Consumer Reports stated that the mean time for a Chrysler Concorde to go from 0 to 60 miles per hour was 8.7 seconds.

A. If you want to set up a statistical test to challenge the clair of 8.7 seconds, what would you use the null hypothesis?

Null Hypothesis: The mean time for a Chrysler Concorde to go from 0 to 60 miles per hour is 8.7 seconds

B. The town of Leadville, Colorado, has an elevation over 10,000 feet, Suppose that you wanted to test the claim that the average time to accelerate from 0 to 60 miles per hour is longer in Leadville (because of less oxygen). What would you use for the alternate hypothesis?

C. Suppose that you made an engine modification and you think the average time to accelerate fro 0 to 60 miles per hour is reduced. What would yu use for the alternate hypothesis?

D. For each of the tests in parts (b) and (c), would the critical region be on the left, right, or both sides of the mean? Explain your answer in each case.

On part (b), the critical region would be on the right side of the mean, this is because when we convert the mean of the sample to a z score using the formula:

, the result would be positive because the (sample mean) would be greater than (population mean), therefore the critical region would be positive (greater than the mean)

On part C, the result would be negative because the (sample mean) would be smaller than (population mean), therefore the critical region would be negative (smaller than the mean)

Problem#3

For problems 3,4,and 5 please provide the requested information.

a. What is the null hypothesis? What is the alternate hypothesis? Will we use a left-tailed, right-tailed, or two tailed test: What is the level of significance?

b. What sampling distribution will we use? What is the critical valueZo(or critical values +over_Zo)?

c. Sketch the critical region and show ...

#### Solution Summary

The solution includes a word document that address, in detailed steps, the requirements of the problem. The spread sheet shows the calculations of means and standard deviations for some of the problems.