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Chapter 8: Q. 9.74 (page 380)

We have been provided a scenario for a hypothesis test for a population mean. Decide whether the z-test is an appropriate method for conducting the hypothesis test. Assume that the population standard deviation is known in the given case.

A normal probability plot of the sample data shows no outliers and is quite linear. The sample size is 12.

Short Answer

Expert verified

The use of the z-test is appropriate.

Step by step solution

01

Step 1. Given information.

Consider the given question,

The sample size is12.

02

Step 2. Consider the given size.

First, we need to make sure that the z-test procedure is suitable for the given sample size. To use the z-test, we need to take care of the following conditions,

In case the sample size isn<15, then the z-test procedure can be used when the variable is very close to being normally distributed or normally distributed.

If the sample size is between15<n<30, then the z-test procedure can be used when there is no outlier in the data or the variable is far from being normally distributed.

If the sample size is greater than 30<n, then the z-test procedure can be used without any limitation.

Here, the given sample size is small. This means, the sample size nis 12<30.

As the variable is very close to being normally distributed or normally distributed.

Hence, the use of the z-test is appropriate.

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Most popular questions from this chapter

Critical Values. In Exercises 21鈥�24, refer to the information in the given exercise and do the following.

a. Find the critical value(s).

b. Using a significance level of = 0.05, should we reject H0or should we fail to reject H0?

Exercise 20

Calculating Power Consider a hypothesis test of the claim that the Ericsson method of gender selection is effective in increasing the likelihood of having a baby girl, so that the claim is p>0.5. Assume that a significance level of 伪= 0.05 is used, and the sample is a simple random sample of size n = 64.

a. Assuming that the true population proportion is 0.65, find the power of the test, which is the probability of rejecting the null hypothesis when it is false. (Hint: With a 0.05 significance level, the critical value is z = 1.645, so any test statistic in the right tail of the accompanying top graph is in the rejection region where the claim is supported. Find the sample proportion in the top graph, and use it to find the power shown in the bottom graph.)

b. Explain why the green-shaded region of the bottom graph represents the power of the test.

In Exercises 13鈥�16, refer to the exercise identified and find the value of the test statistic. (Refer to Table 8-2 on page 362 to select the correct expression for evaluating the test statistic.)

Exercise 6 鈥淐ell Phone鈥�

Testing Claims About Proportions. In Exercises 9鈥�32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.

Stem Cell Survey Adults were randomly selected for a Newsweek poll. They were asked if they 鈥渇avor or oppose using federal tax dollars to fund medical research using stem cells obtained from human embryos.鈥� Of those polled, 481 were in favor, 401 were opposed, and 120 were unsure. A politician claims that people don鈥檛 really understand the stem cell issue and their responses to such questions are random responses equivalent to a coin toss. Exclude the 120 subjects who said that they were unsure, and use a 0.01 significance level to test the claim that the proportion of subjects who respond in favor is equal to 0.5. What does the result suggest about the politician鈥檚 claim?

Final Conclusions. In Exercises 25鈥�28, use a significance level of = 0.05 and use the given information for the following:

a. State a conclusion about the null hypothesis. (Reject H0or fail to reject H0.)

b. Without using technical terms or symbols, state a final conclusion that addresses the original claim.

Original claim: More than 58% of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of 0.3257.
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