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StatisticsQ&A LibrarySuppose a company claims that its market share is less than 16 percent, on average. Several of coworkers do not believe this, so a director decides to do a hypothesis test, at a 1% significance level, to persuade them. He conducts 21 surveys, collects the proper data, and works through the testing procedure:H0: μ≥16; Ha: μ<16x¯=15.8σ=1.8α=0.01 (significance level)The test statistic isz0=x¯−μ0σn√=15.8−161.821√=−0.51The critical value is −z0.01=−2.33.Conclude whether to reject or not reject H0, and interpret the results. Select the correct answer below: Reject H0. At the 1% significance level, the test results are not statistically significant and at best, provide weak evidence against the null hypothesis. Reject H0. At the 1% significance level, the data provide sufficient evidence to conclude that the mean market share is less than 16 percent. Do not reject H0. At the 1% significance level, the test results are not statistically significant and at best, provide weak evidence against the null hypothesis. Do not reject H0. At the 1% significance level, the data provide sufficient evidence to conclude that the mean market share is less than 16 percent.Question

Asked Mar 19, 2019

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Suppose a company claims that its market share is less than 16 percent, on average. Several of coworkers do not believe this, so a director decides to do a hypothesis test, at a 1% significance level, to persuade them. He conducts 21 surveys, collects the proper data, and works through the testing procedure:

- H0: μ≥16; Ha: μ<16
- x¯=15.8
- σ=1.8
- α=0.01 (significance level)
- The test statistic is
z0=x¯−μ0σn√=15.8−161.821√=−0.51
- The critical value is −z0.01=−2.33.

Conclude whether to reject or not reject H0, and interpret the results.

Select the correct answer below:

Reject H0. At the 1% significance level, the test results are not statistically significant and at best, provide weak evidence against the null hypothesis.

Reject H0. At the 1% significance level, the data provide sufficient evidence to conclude that the mean market share is less than 16 percent.

Do not reject H0. At the 1% significance level, the test results are not statistically significant and at best, provide weak evidence against the null hypothesis.

Do not reject H0. At the 1% significance level, the data provide sufficient evidence to conclude that the mean market share is less than 16 percent.

Step 1

The level of significance is 0.01.

The test statistic is *z* = -0.51.

The critical value is -2.33.

This test is a left tailed test.

*Decision rule:*

For positive test statistic, if , reject the null hypothesis, otherwise fail to reject the null hypothesis.

For negative test statistic, if , reject the null hypothesis, otherwise fail to reject the null hypothesis.

Step 2

*Conclusion:*

Here z = -0.51, critical value z_{α} = -2.33.

Therefore, the test statistic is not less than the critical value.

That is, -0.51 > -2.33.

Using the decision rule, fail to reject the null hypothesis at 1% level of significance.

Hence, it can be concluded that there is no sufficient evidence to conclude that the market share is less than 16% at 1% level of significance.

Step 3

Therefore, from the given option, the **third interpretation** is correct.

Now, the 1st interpretation contradicts the 3rd interpretation. This means that the 1st interpretation must be **incorrect** when the 3rd interpretation is correct.

In similar way, 2nd interpretation contradicts the 3rd interpretation. This means that the 2nd interpretation must be **incorrect** when the 3rd interpretation is correct....

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