# Proportion of Sample Who Enjoy Shopping

Sample question:

A sample of 500 shoppers were selected in a large metropolitan to determine various information concerning consumer behavior. Among the questions asked was, "Do you enjoy shopping for clothing?"

The results are summarized in the following contigency table:

Enjoy Shopping for Clothing MALE FEMALE TOTAL

YES 136 224 360

NO 104 36 140

TOTAL 240 260 500

a) Is there evidence of a significant difference between the proportion males and females who enjoy shopping for clothing at the 0.01 level of significance?

b) Determine the p-value in (a) and interpret its meaning

c) What are your answers to (a) and (b) if 206 males enjoyed shopping for cloting and 34 did not?

https://brainmass.com/statistics/hypothesis-testing/proportion-of-sample-who-enjoy-shopping-536172

#### Solution Preview

Answers

a. Is there evidence of a significant difference between the proportion of males and females who enjoy shopping for clothing at the 0.01 level of significance?

The null hypothesis tested is

H0: There is no significant difference between the proportion of males and females who enjoy shopping for clothing.

The alternative hypothesis is

H1: There is significant difference between the proportion of males and females who enjoy shopping for clothing.

The test statistic used is x^2 = sum of (O - E) / E = 0.010648266 where O is the observed frequency and E is the expected frequency.

The Expected frequencies are given below. They are calculated using the formula, , where Ri , ith row total, Cj jth column total and G is the grand Total.

Rejection Criteria: Reject the null hypothesis, if the calculated value of chi square is greater than the critical value of Chi square with 1 d.f. at 0.01 significance level.

The observed and expected frequencies are given in the tab Qn. a.

Test statistic, x^2 = sum of (O - E) / E = ...

#### Solution Summary

Level of Significance for Proportion of Sample Who Enjoy Shopping

Business Statistics using PHSTAT add-in

See attached: Must use Excel with the PHSTAT add-in, and then paste all into MS Word.

The manager of a paint supply store wants to determine whether the amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer actually averages 1gallon. It is known from the manufacturer's specifications that the standard deviation of the amount of paint is equal to .02 gallon. A random sample of 50 cans is selected, and the mean of the amount of paint per 1-gallon can is found to be .995 gallon.

See attached file for full problem description.

Must use Excel with the PHSTAT add-in and then paste all into MS Word

Template

Problem #1 The manager of a paint supply store wants to determine whether the amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer actually averages 1gallon. It is known from the manufacturer's specifications that the standard deviation of the amount of paint is equal to .02 gallon. A random sample of 50 cans is selected, and the mean of the amount of paint per 1-gallon can is found to be .995 gallon.

a. State the null (N) and the hypotheses (H).

? _______________________________________

b. Is there evidence that the mean amount is different from 1.0 gallon (use alpha .01).

? _______________________________________

c. Interpret the meaning of the p-value.

? ________________________________________

Problem #2 The policy of a particular bank branch is that the ATMs must be stocked with enough cash to satisfy customers making withdrawals over an entire weekend. Customer goodwill depends on such services meeting customer needs. At this branch the expected (i.e., population) mean amount of money withdrawn from ATMs per customer transaction over the weekend is $160, with an expected (i.e., population) standard deviation of $30. Suppose that a random sample of 36 customer transactions is examined and it is observed that the sample mean withdrawal is $172

a. At the a .05 significance level, using the critical value approach to hypothesis testing, is there evidence that the true mean withdrawal is GREATER than $160?

? __________________________________________

b. At the a .05 significance level, using the p- value approach to hypothesis testing, is there evidence that the true mean withdrawal is GREATER than $160?

? ___________________________________________:

Problem #3 More professional women than ever are foregoing motherhood because of the time constraints of their careers. Yet, many women still manage to find time to climb the corporate ladder and set time aside to have children. A survey of 187 attendees at Fortune Magazine's Most Powerful Women summit in March 2002 found that 133 had at least one child (Carol Hymowitz " Women Plotting Mix of Work & Family Won't Find Perfect Plan, Wall Street Journal, June 11, 2002 B1) Assume that the group of 187 is a random sample from the population of all successful women executives.

a. What is the sample proportion of women executives who have children?

? ____________________________________________

b. At the .05 level of significance, can you state that more than one half of all successful women executives have children?

? ____________________________________________

c. At the .05 level of significance, can you state that more than two thirds of all successful women executives have children?

? _____________________________________________

d. Do you think the random sample assumption is valid?

? ________________________________________________

Problem #4 The data below represent the compressive strength in thousands of pounds per square inch (psi) of 40 samples of concrete taken two and seven days after pouring.

Sample Two days Seven days Sample Two days Seven days

1 2.83 3.505 21 1.635 2.275

2 3.295 3.43 22 2.27 3.91

3 2.71 3.67 23 2.895 2.915

4 2.855 3.355 24 2.845 4.53

5 2.98 3.985 25 2.205 2.28

6 3.065 3.63 26 3.59 3.915

7 3.765 4.57 27 3.08 3.14

8 3.265 3.7 28 3.335 3.58

9 3.17 3.66 29 3.8 4.07

10 2.895 3.25 30 2.68 3.805

11 2.63 2.85 31 3.76 4.13

12 2.83 3.34 32 3.605 3.72

13 2.935 3.63 33 2.005 2.69

14 3.115 3.675 34 2.495 3.23

15 2.985 3.475 35 3.205 3.59

16 3.135 3.605 36 2.06 2.945

17 2.75 3.25 37 3.425 4.03

18 3.205 3.54 38 3.315 3.685

19 3 4.005 39 3.825 4.175

20 3.035 3.595 40 3.16 3.43

c. At the .01 level of significance, is there evidence that the average strength is less at two days than at seven days?

? ________________________________________________

d. What assumption is necessary to perform this test?

? ________________________________________________

e. Find the p-value and interpret its meaning.

? ________________________________________________

Problem #5 A sample of 500 shoppers was selected in a large metropolitan area to determine various information concerning consumer behavior. Among the questions asked was, "Do you enjoy shopping for clothing?" Of the 240 males, 136 answered yes and of the 260 females, 224 answered yes.

a. Is there evidence of a significant difference between males and females in the proportion who enjoy shopping for clothing, at the .01 level of significance?

? _____________________________________________

b. Find the p-value and interpret its meaning.

? _____________________________________________

c. What would be your answer to A-B if 206 males enjoyed shopping for clothing?

? ______________________________________________

Problem #6 The pet-drug market is growing very rapidly. Before new pet drugs can be introduced into the marketplace, they must be approved by the U.S. Food & Drug Administration (FD). In 1999, the Novartis company was trying to get Anafranil, a drug to reduce dog anxiety, approved. According to an article (Elyse Tanouye, "The Ow in Bowwow: With Growing Market in Pet Drugs, Makers Revamp Clinical Trials." Wall Street Journal, April 13, 1999), Novartis had to find a way to translate a dog's anxiety symptoms into numbers that could be used to prove to the FDA that that the drug had a statistically significant effect on the condition. (PHSTAT not needed for this problem)

a. What is meant by the phrase "statistically significant effect?"

? ________________________________________________________:

b. Consider an experiment where dogs suffering from anxiety are divided into two groups. One group will be given Anafranil, and the other will be given a placebo (a drug without active ingredients). How can a dog's anxiety symptoms be translated into numbers? In other words, does a continuous random variable (X1), the measurement of effectiveness of the drug Ananfranil, and X2, the measurement of effectiveness of the placebo.

? ________________________________________________________

c. Building on your answer to part (b), define the null & hypothesis for the study.

? ______________________________________________________