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Chapter 7: Q67E (page 424)

Refer to Exercise 6.44 (p. 356), in which 50 consumers taste-tested a new snack food. Their responses (where 0 = do not like; 1 = like; 2 = indifferent) are reproduced below

  1. Test \({H_0}:p = .5\) against \({H_0}:p > .5\), where p is the proportion of customers who do not like the snack food. Use \(\alpha = 0.10\).
    1 0 0 1 2 0 1 1 0 0 0 1 0 2 0 2 2 0 0 1 1 0 0 0 0 1 0 2 0 0 0 1 0 0 1 0 0 1 0 1 0 2 0 0 1 1 0 0 0 1

Short Answer

Expert verified
  1. The test statistic is 1.142

Step by step solution

01

Given Information

The number of sample size is 50.

The hypothesis are given by

\(\begin{aligned}{H_0}:p = .5\\{H_a}:p > .5\end{aligned}\)

02

Null hypothesis

A null hypothesis is a statistical supposition that claims there is no difference between specific features of a population as well as data-generating activity. The alternate hypothesis asserts that there is a distinction. Hypothesis test enables you to reject a null hypothesis with a particular confidence level.

03

Testing of hypothesis

The proportion of customers who do not like the snack food is given below

\(\begin{aligned}\hat p &= \frac{{29}}{{50}}\\ &= 0.58\end{aligned}\)

The test statistic is calculated as

\(\begin{aligned}z &= \frac{{\hat p - p}}{{\sqrt {\frac{{pq}}{n}} }}\\ &= \frac{{0.58 - 0.5}}{{\sqrt {\frac{{.5 \times .5}}{{50}}} }}\\ &= \frac{{0.08}}{{0.07}}\\ &= 1.142\end{aligned}\)

Therefore, the test statistic is 1.142.

Rejection region \(z > {z_{0.1}} = 1.282\)

Therefore, the calculated z-value does not fall in the rejection region. We do not reject the null hypothesis.

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Most popular questions from this chapter

Manufacturers that practice sole sourcing. If a manufacturer (the vendee) buys all items of a particular type from a particular vendor, the manufacturer is practicing sole sourcing (Schonberger and Knod, Operations Management, 2001). As part of a sole-sourcing arrangement, a vendor agrees to periodically supply its vendee with sample data from its production process. The vendee uses the data to investigate whether the mean length of rods produced by the vendor's production process is truly 5.0 millimetres (mm) or more, as claimed by the vendor and desired by the vendee.

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b. Refer to part a. What is the probability that the vendee's test will reject the null hypothesis when m = 5.0? What is the name given to this Type of error?

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c. Locate values of the test statistic and corresponding p-value on the printout.

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