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Chapter 7: Q122SE (page 442)

鈥淢ade in the USA鈥� survey. Refer to the Journal of Global Business (Spring 2002) study of what 鈥淢ade in the USA鈥� means to consumers, Exercise 2.154 (p. 143). Recall that 64 of 106 randomly selected shoppers believed 鈥淢ade in the USA鈥� means 100% of labor and materials are from the United States. Let p represent the true proportion of consumers who believe 鈥淢ade in the USA鈥� means 100% of labor and materials are from the United States.

a. Calculate a point estimate for p.

Short Answer

Expert verified

a. The point estimate of p is 0.604.

Step by step solution

01

Given Information

From Exercise 2.154,

The total number of shoppers, n=106.

The responses of the 106 shoppers are summarized as follows:

Number of shoppers

Response percentage

64

100%

20

75% to 99%

18

50% to 74%

4

<50%

02

State the large sample test of the hypothesis about a population proportion.

The condition required for a valid large sample hypothesis test for p is:

  • The sample size n is large. (This condition will be satisfied if both \(n{p_0} \ge 15\) and \(n{q_0} \ge 15\))
  • The random sample is selected from a binomial population.
03

Compute the point estimate of p.

a.

Let p represents the true proportion of consumers who believe 100% of labor and material are from the United States.

The number of shoppers who believe 100% of labor and material, x=64.

The total number of shoppers, n=106.

The point estimate of p is computed as:

\(\begin{aligned}p &= \frac{x}{n}\\ &= \frac{{64}}{{106}}\\ &= 0.604\end{aligned}\)

Hence, the point estimate of p is 0.604.

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Most popular questions from this chapter

Student loan default rate. The national student loan default rate has fluctuated over the past several years. Recently (October 2015) the Department of Education reported the default rate (i.e., the proportion of college students who default on their loans) at 0.12. Set up the null and alternative hypotheses if you want to determine if the student loan default rate this year is less than 0.12.
The testing claimed by the national student loan default rate is the test for a specified proportion.

Complete the following statement: The smaller the p-value associated with a test of hypothesis, the stronger the support for the _____ hypothesis. Explain your answer.

Performance of stock screeners. Recall, from Exercise 6.36 (p. 350), that stock screeners are automated tools used by investment companies to help clients select a portfolio of stocks to invest in. The data on the annualized percentage return on investment (as compared to the Standard & Poor鈥檚 500 Index) for 13 randomly selected stock screeners provided by the American Association of Individual Investors (AAII) are repeated in the accompanying table. You want to determine whether \(\mu \) , the average annualized return for all AAII stock screeners, is positive (which implies that the stock screeners perform better, on average, than the S&P 500). An XLSTAT printout of the analysis is shown on the top of page 418.

9.0 -.1 -1.6 14.6 16.0 7.7 19.9 9.8 3.2 24.8 17.6 10.7 9.1

  1. State \({H_0}\,and\,{H_a}\) for this test

A two-tailed test was conducted with the null and alternative hypotheses stated being \({H_0}:p = .69\) against \({H_a}:p \ne .69\), respectively, with a sample size of 150. The test results were z = -.98 and two-tailed p-value = .327

a. Determine the conditions required for a valid large sample test

: A random sample of n = 200 observations from a binomial population yield

p^=0.29

a. Test H0:p=0.35 against H0:p<0.35. Usea=0.05.
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