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Chapter 7: Q122SE (page 442)

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