In: Statistics and Probability
The mean number of close friends for the population of people living in the U.S. is 5.7. The standard deviation of scores in this population is 1.3. An investigator predicts that the mean number of close friends for introverts will be significantly different from the mean of the population. The mean number of close friends for a sample of 26 introverts is 6.5. Do these data support the investigator's prediction? Use 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.