Question

The mean Verbal SAT score for the population of first students at Radford is 520. The standard deviation of scores in this population is 95. An investigator believes that the mean Verbal SAT of first year psychology majors is significantly different from the mean score of the population. The mean of a sample of 36 first year psychology majors is 548. Please test the investigator's prediction using an alpha level of .05.

a. Please state both the null and alternative hypotheses.

b. Please determine the critical region.

c. Please show all calculations needed to generate the appropriate statistic.

d. State your decision as to whether the investigator should reject the null hypothesis.

e. State the conclusion the investigator is entitled to draw.

Answer 1

Here we have n = 36, = 548, = 95, = 0.05

a) The hypothesis are

H0: = 520 v/s H1: 520  

b) The critical region :

Here test is two tailed.

Hence critical values are :

c. The test statistic is given by

= 1.77

d. Here calculated value of z does not lie in the critical region. Hence we failed to reject null hypothesis.

e. We conclude that an investigator believes that the mean Verbal SAT of first year psychology majors is significantly different from the mean score of the population.