Question

The mean number of close friends for the population of people living in the U.S. is 5.7. An investigator predicts that the mean number of close friends for introverts will be significantly less than the mean of the population. The mean number of close friends for a sample of 30 introverts is 6.5, with a standard of 1.3. Using a level of significance of .01, and the six-step approach, test whether the data support the investigator’s prediction.

NOTE: The steps must be clearly and neatly indicated. (2, 5, 3, 8, 3, 4 = 25 points)

Answer 1

Here claim is that

Hence hypothesis is vs

As population standard deviation is not known, we will use t distribution to find test statistics

The t-critical value for a left-tailed test, for a significance level of α=0.01 is

tc​=−2.462

Graphically

As t statistics do not fall in the rejection region, we fail to reject the null hypothesis

Hence we do not have sufficient evidence to support the clain that mean is less than the mean of the population.