Question

Let x be a randon variable representing dividend yield of Australian bank stocks, we may assume that x has a normal distribution with σ = 2.6%. A random sample of 17 Australian bank stocks has a sample mean or 8.76%. For the entire Australian stock market, the mean dividend yield is μ 6.5 Do these data indicate that the dividend yield of all Australian bank stocks is higher than 6.5%? Use α 0.01 Are the data statistically significant at the given level of significance? Based on your answers, will you reject or fail to reject the null hypothesis? Select one: a. The P-value is less than than the level of significance and so the data are statistically significant. Thus, we reject the null hypothesis. b. The P-value is less than than the level of significance and so the data are statistically significant. Thus, we fail to reject the null hypothesis. C. The P-value is less than than the level of significance and so the data are not statistically significant. Thus, we reject the null hypothesis. O d. The P-value is greater than than the level of significance and so the data are not statistically significant. Thus, we fail to reject the ull hypothesis. e. The P-value is greater than than the level of significance and so the data are statistically significant. Thus, we reject the null hypothesis.

Answer 1

Answer : Option ( a )

The p value is less the level of significance and so the data are statistically significant .Thus we reject the null hypothesis

Explanation :

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ ≤ 6.5

Ha: μ > 6.5 ( claim )

Test Statistics

The z-statistic is computed as follows:

Using the P-value approach:

The p-value is p = 0.0002, and since p = 0.0002 < 0.01, it is concluded that the null hypothesis is rejected.

Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is greater than 6.5, at the 0.01 significance level.