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 17 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 6.7%? 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

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 17 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 6.7%? 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 6.7%, we need to conduct a hypothesis test using the given data.

Here are the steps to follow:

Step 1: State the null hypothesis (H0) and the alternative hypothesis (Ha):
- Null hypothesis (H0): The dividend yield of all Australian bank stocks is not higher than 6.7%.
- Alternative hypothesis (Ha): The dividend yield of all Australian bank stocks is higher than 6.7%.

Step 2: Choose the level of significance (α):
- The significance level, α, represents the likelihood of rejecting the null hypothesis when it is actually true. The commonly used levels are 0.05 (5%) or 0.01 (1%). Let's assume α = 0.05 for this explanation.

Step 3: Calculate the test statistic:
- Since we know the population standard deviation is , and the sample size is n = 17, we can calculate the standard error (SE) as:
SE = / sqrt(n)

Step 4: Calculate the t-value:
- The t-value can be calculated by taking the difference between the sample mean and the hypothesized population mean (6.7%) divided by the standard error.
t = (sample mean - hypothesized mean) / SE

Step 5: Determine the critical value:
- For a one-tailed t-test, with α = 0.05 and degrees of freedom (n-1) = 16, the critical value for rejection is 1.74.

Step 6: Compare the t-value with the critical value:
- If the calculated t-value is greater than the critical value, we can reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Step 7: Make a conclusion:
- If we reject the null hypothesis, it indicates that the dividend yield of all Australian bank stocks is higher than 6.7% at a significance level of 0.05. If we fail to reject the null hypothesis, it means there is not enough evidence to conclude that the dividend yield is higher than 6.7%.

By following these steps and plugging in the given values, you can evaluate whether the data is statistically significant and decide to reject or fail to reject the null hypothesis.