1215

Given the following hypothesis:

• The null hypothesis is H₀ : μ = 5
• The alternative is H₁ : μ ≠ 5
• The mean of a sample of 17 is 7
• The population standard deviation is 2.0

What is the calculated z-statistic?

A) 4.12.

B) 4.00.

C) 8.00.

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The z-statistic is calculated by subtracting the hypothesized parameter from the parameter that has been estimated and dividing the difference by the standard error of the sample statistic. Here, the test statistic = (sample mean ? hypothesized mean) / (population standard deviation / (sample size)^1/2 = (X ? μ) / (σ / n^1/2) = (7 ? 5) / (2 / 17^1/2) = (2) / (2 / 4.1231) = 4.12.

1215

What kind of test is being used for the following hypothesis and what would a z-statistic of 1.68 tell us about a hypothesis with the appropriate test and a level of significance of 5%, respectively?

H₀: B ≤ 0
H_A: B > 0

A) One-tailed test; fail to reject the null.

B) Two-tailed test; fail to reject the null.

C) One-tailed test; reject the null.

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The way the alternative hypothesis is written you are only looking at the right side of the distribution. You are only interested in showing that B is greater than 0. You don't care if it is less than zero. For a one-tailed test at the 5% level of significance, the critical z value is 1.645. Since the test statistic of 1.68 is greater than the critical value we would reject the null hypothesis.

1215

In a two-tailed test of a hypothesis concerning whether a population mean is zero, Jack Olson computes a t-statistic of 2.7 based on a sample of 20 observations where the distribution is normal. If a 5% significance level is chosen, Olson should:

A) reject the null hypothesis and conclude that the population mean is significantly different from zero.

B) reject the null hypothesis and conclude that the population mean is not significantly different from zero.

C) fail to reject the null hypothesis that the population mean is not significantly different from zero.

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At a 5% significance level, the critical t-statistic using the Student’s t-distribution table for a two-tailed test and 19 degrees of freedom (sample size of 20 less 1) is ± 2.093 (with a large sample size the critical z-statistic of 1.960 may be used). Because the critical t-statistic of 2.093 is to the left of the calculated t-statistic of 2.7, meaning that the calculated t-statistic is in the rejection range, we reject the null hypothesis and we conclude that the population mean is significantly different from zero.

1215

In order to test whether the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken and the sample value of the computed test statistic, t_n-1 = 3.4. The null and alternative hypotheses are:

A) H0: μ = 100; Ha: μ ≠ 100.

B) H0: X ≤ 100; Ha: X > 100.

C) H0: μ ≤ 100; Ha: μ > 100.

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The null hypothesis is that the theoretical mean is not significantly different from zero. The alternative hypothesis is that the theoretical mean is greater than zero.

1215

In order to test if the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken and the sample value of the computed test statistic, t_n-1 = 1.2. If you choose a 5% significance level you should:

A) fail to reject the null hypothesis and conclude that the population mean is not greater than 100.

B) reject the null hypothesis and conclude that the population mean is greater than 100.

C) fail to reject the null hypothesis and conclude that the population mean is greater than 100.

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At a 5% significance level, the critical t-statistic using the Student’s t distribution table for a one-tailed test and 29 degrees of freedom (sample size of 30 less 1) is 1.699 (with a large sample size the critical z-statistic of 1.645 may be used). Because the critical t-statistic is greater than the calculated t-statistic, meaning that the calculated t-statistic is not in the rejection range, we fail to reject the null hypothesis and we conclude that the population mean is not significantly greater than 100.

1215

If the null hypothesis is H₀: ρ ≤ 0, what is the appropriate alternative hypothesis?

A) Ha: ρ ≠ 0.

B) Ha: ρ < 0.

C) Ha: ρ > 0.

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The alternative hypothesis must include the possible outcomes the null does not.

1215

Jo Su believes that there should be a negative relation between returns and systematic risk. She intends to collect data on returns and systematic risk to test this theory. What is the appropriate alternative hypothesis?

A) Ha: ρ > 0.

B) Ha: ρ ≠ 0.

C) Ha: ρ < 0.

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The alternative hypothesis is determined by the theory or the belief. The researcher specifies the null as the hypothesis that she wishes to reject (in favor of the alternative). The theory in this case is that the correlation is negative.

1215

Jill Woodall believes that the average return on equity in the retail industry, μ, is less than 15%. What are the null (H₀) and alternative (H_a) hypotheses for her study?

A) H0: μ ≤ 0.15 versus Ha: μ > 0.15.

B) H0: μ ≥ 0.15 versus Ha: μ < 0.15.

C) H0: μ < 0.15 versus Ha: μ ≥ 0.15.

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This is a one-sided alternative because of the "less than" belief.

1215

Brian Ci believes that the average return on equity in the airline industry, μ, is less than 5%. What are the appropriate null (H₀) and alternative (H_a) hypotheses to test this belief?

A) H0: μ < 0.05 versus Ha: μ ≥ 0.05.

B) H0: μ ≥ 0.05 versus Ha: μ < 0.05.

C) H0: μ < 0.05 versus Ha: μ > 0.05.

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The alternative hypothesis is determined by the theory or the belief. The researcher specifies the null as the hypothesis that he wishes to reject (in favor of the alternative). Note that this is a one-sided alternative because of the "less than" belief.

1215

George Appleton believes that the average return on equity in the amusement industry, μ, is greater than 10%. What is the null (H₀) and alternative (H_a) hypothesis for his study?

A) H0: > 0.10 versus Ha: ≤ 0.10.

B) H0: > 0.10 versus Ha: < 0.10.

C) H0: ≤ 0.10 versus Ha: > 0.10.

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The alternative hypothesis is determined by the theory or the belief. The researcher specifies the null as the hypothesis that he wishes to reject (in favor of the alternative). Note that this is a one-sided alternative because of the "greater than" belief.