Question

Question 5 of 8 The Wechsler Adult Intelligence Scale (IQ test) is constructed so that Full Scale IQ scores follow a normal distribution, with a mean of 100, and a standard deviation of 15. Dr.Smartyskirt is a University professor and believes that university professors are smarter than the national average and wants to use it (the intelligence of the professors) as a marketing tool to bring new students to the University. A researcher is hired to conduct a study to determine whether University professors, on average, have higher Full Scale IQs than the population. A random sample of 100 professors from various Universities were given the IQ test and were found to have an average Full Scale IQ of 140. Which hypothesis test should be used to determine whether the mean Full Scale IQ score of the professors is higher than the national average? z-test for the population mean, t-test for the population mean, z-test for the population proportion, t-test for the population proportion

Question 6 of 8 What are the null and alternative hypotheses? H0: μ = 100 Ha: μ > 100 H0: μ = 100 Ha: μ ≠ 100 H0: μ = 140 Ha: μ > 140 H0: μ = 140 Ha: μ ≠ 140

Question 7 of 8 What is the value of the test statistic used to determine whether the mean Full Scale IQ score of the University professors is higher than the national average? 26.67 -26.67 2.67 -2.67

Question 8 of 8 After analyzing the data to determine whether the mean Full Scale IQ score of the University professors is higher than the national average, the P-value of < .00001 was obtained. Using a .05 significance level, what conclusion can be drawn from the data?

Reject the null hypothesis. The average Full Scale IQ of the University professors is higher than the population average. Do not reject the null hypothesis. The average Full Scale IQ of the University professors is not higher than the population average.

Do not reject the null hypothesis. The average Full Scale IQ of the University professors is higher than the population average.

Reject the null hypothesis. The average Full Scale IQ of the University professors is not higher than the population average.

Answer 1

z-test for the population mean

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

NULL HYPOTHESIS Ho:μ=100

ALTERNATIVE HYPOTHESIS Ha: μ>100

This corresponds to a right-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a right-tailed test is zc​=1.64.

The rejection region for this right-tailed test is R={z:z>1.64}

(3) Test Statistics : z-test for the population mean (Population standard deviation known)

The z-statistic is computed as follows:

Test statistic Z= 26.67

Decision about the null hypothesis

Since it is observed that z=26.667>zc​=1.64, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0.000, and since p=0<0.05, it is concluded that the null hypothesis is rejected.

Reject the null hypothesis. The average Full Scale IQ of the University professors is higher than the population average.