Answer:
The 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32, 4.84).
Yes, this confidence interval contradict the belief that it takes 4 years to complete a bachelor’s degree.
Step-by-step explanation:
The (1 - <em>α</em>)% confidence interval for population mean <em>μ, </em>when the population standard deviation is not known is:
The information provided is:
Compute the critical value of <em>t</em> for 90% confidence interval and (n - 1) degrees of freedom as follows:
*Use a <em>t</em>-table for the probability.
Compute the 90% confidence interval for population mean <em>μ</em> as follows:
Thus, the 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32, 4.84).
If a hypothesis test is conducted to determine whether it takes 4 years to complete a bachelor’s degree or not, the hypothesis will be:
<em>Hₐ</em>:<em> </em>The mean time it takes to complete a bachelor’s degree is 4 years, i.e. <em>μ </em>= 4.
<em>Hₐ</em>:<em> </em>The mean time it takes to complete a bachelor’s degree is different from 4 years, i.e. <em>μ </em>≠ 4.
The decision rule based on a confidence interval will be:
Reject the null hypothesis if the null value is not included in the interval.
The 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32 years, 4.84 years).
The null value, i.e. <em>μ </em>= 4 is not included in the interval.
The null hypothesis will be rejected at 10% level of significance.
Thus, it can be concluded that that time it takes to complete a bachelor’s degree is different from 4 years.