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In: Statistics and Probability

1.) (Be Sure to fill out full 6 steps number them) Q: A college admissions officer...

1.) (Be Sure to fill out full 6 steps number them)

Q: A college admissions officer for the school’s online undergraduate program wants to estimate the mean age of its graduating students. The administrator took a random sample of 40 from which the mean was 24 years and the standard deviation was 1.7 years.

If the mean age of online undergraduate students was 23 years of age, what is the probability that the sample of 40 would have produced a mean age of 24 or higher? Be sure to set up the two competing hypotheses and provide a statistical conclusion statement at a 5% level of significance for your results.

Solutions

Expert Solution

The provided sample mean is and the sample standard deviation is , and the sample size is

The following null and alternative hypotheses need to be tested:

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

Based on the information provided, the significance level is , and the critical value for a right-tailed test is

The rejection region for this right-tailed test is

The t-statistic is computed as follows:

Since it is observed that , it is then concluded that the null hypothesis is rejected.

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean is greater than 23, at the 0.05 significance level.

orchestra answered 1 year ago
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