Question

In: Statistics and Probability

The Basic Steps to Calculating a Hypothesis Test You want to start by determining whether you...

The Basic Steps to Calculating a Hypothesis Test

You want to start by determining whether you are interested in working with a mean or a proportion. Then identify each of the parts listed below.

  1. In order to use the formulas for a hypothesis test we first need to confirm that the sample size requirements for the central limit theorem are satisfied. See the notes for more information. If the sample size is not met acknowledge that you need to proceed with caution.
  2. Identify the null and alternative hypotheses. The null hypothesis will be listed first. When working with a proportion the hypothesis will include that symbol for the population proportion, p. When working with a mean the hypothesis will include that symbol for the population mean, µ.
  3. Calculate the appropriate test statistic. When working with proportions you will calculate a z-statistic. When working with means you will calculate a t-statistic.
  4. Compare your test statistic to the appropriate distribution to find the p-value.
  5. Conclude the test in context of the problem.

For each of the four problems below provide all of the steps listed above. Complete all of the work by hand and show your work. You may use the applications listed in the notes to check your work.

3. According to https://news.gallup.com/poll/235280/americans-say-pornography-morally-acceptable.aspx , dated June 5, 2018, a poll conducted by Gallup asked 1024 randomly selected U.S. adults whether they believe pornography was morally acceptable. Assume that 440 survey respondents said they believe pornography was morally acceptable. Is there evidence that fewer than 40% of adults in the U.S. believe pornography is morally acceptable? Perform the hypothesis test using a 5% significance level.

Solutions

Expert Solution

The critical one tailed value of test statistic at significance level of 0.05 for a left tailed test is -

Z0.05 = -1.645

As the calculated value of test statistic is greater than the critical value, thus we fail to reject the null hypothesis and conclude that there is not enough evidence in the data to support the claim that the population proportion of U.S adults who believe pornography was morally acceptable is not less than 40%.


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