4. Let X be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with A random sample of 19 Australian bank stocks has a sample mean of For the entire Australian stock market, the mean dividend yield is Do these data indicate that the dividend yield of all Australian bank stocks is higher than 5.9%? Use 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?

Question

4. Let X be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with A random sample of 19 Australian bank stocks has a sample mean of For the entire Australian stock market, the mean dividend yield is Do these data indicate that the dividend yield of all Australian bank stocks is higher than 5.9%? Use 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?

Answer 1

To determine whether the dividend yield of all Australian bank stocks is higher than 5.9%, we need to perform a hypothesis test.

1. State the hypotheses:

Null hypothesis (H₀): The mean dividend yield of all Australian bank stocks is 5.9% or less.
Alternate hypothesis (H₁): The mean dividend yield of all Australian bank stocks is higher than 5.9%.

2. Set the level of significance:

Let's assume the level of significance (alpha) as 0.05, which is a common choice.

3. Compute the test statistic:

Since we know the population standard deviation is unknown, but the sample size is > 30, we can use a one-sample t-test. The test statistic formula is:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Given information:
Sample mean (x̄) =
Population mean (μ) =
Sample standard deviation (s) =
Sample size (n) =

t = ( - ) / ( / sqrt())

4. Determine the critical value:

The critical value is based on the chosen level of significance and the degrees of freedom. Since we have a sample size of 19, the degrees of freedom for a one-sample t-test is n-1 = 19-1 = 18. You can use a t-distribution table or a statistical software to find the critical value associated with a one-tailed test at alpha=0.05 and 18 degrees of freedom.

5. Compare the test statistic with the critical value:

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the dividend yield of all Australian bank stocks is higher than 5.9%. If the test statistic is less than or equal to the critical value, we fail to reject the null hypothesis.

6. Make the decision:

Based on the test statistic and critical value comparison, decide whether to reject or fail to reject the null hypothesis.

Note: Since you did not provide the sample mean and sample standard deviation, it is not possible to provide a definitive answer to whether the data is statistically significant or to reject/fail to reject the null hypothesis.