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.
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.
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