Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with \alpha =2.3% A random sample of 18 Australian bank stocks has a sample mean of x bar = 6.1%. For the entire Australian stock market, the mean dividend yield is \mu = 5.5%. Do these data indicate that the dividend yield of all Australian bank stocks is higher than 5.5%? Use \alpha 6.1%What is the value of the test statistic?

Question

Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with \alpha =2.3% A random sample of 18 Australian bank stocks has a sample mean of x bar = 6.1%. For the entire Australian stock market, the mean dividend yield is \mu = 5.5%. Do these data indicate that the dividend yield of all Australian bank stocks is higher than 5.5%? Use \alpha 6.1%What is the value of the test statistic?

a. 1.109
b. 1.107
c. –0.261
d. 0.061

Answer 1

To determine the value of the test statistic, we need to perform a hypothesis test using the given data.

The null hypothesis (H0) states that the dividend yield of all Australian bank stocks is equal to 5.5%. The alternative hypothesis (Ha) states that the dividend yield is higher than 5.5%.

In this case, we have a one-sample t-test because we have a sample mean and we are comparing it to a known population mean.

The formula to calculate the test statistic for a one-sample t-test is:

t = (x̄ - μ) / (s / √n)

Where:
x̄ is the sample mean (6.1%)
μ is the population mean (5.5%)
s is the sample standard deviation (unknown in this case)
n is the sample size (18)

Given that the population mean (μ) and sample mean (x̄) are in percentages, we need to convert them to decimal form before calculating the test statistic.

μ = 5.5% = 0.055
x̄ = 6.1% = 0.061

We already have the value of α (alpha) as 0.061, but it is actually the significance level (usually denoted as α). The value of α is not the test statistic.

Now, plug in the values into the formula:

t = (0.061 - 0.055) / (s / √18)

Since the sample standard deviation (s) is not provided, we cannot calculate the exact test statistic. Therefore, we need additional information to proceed.

To make a decision about whether the dividend yield is higher than 5.5%, we would need the critical value or the p-value associated with the test statistic at the given significance level (α). Without these values, we cannot determine the test statistic or make a definitive conclusion.

Therefore, the value of the test statistic cannot be determined from the given information.