1 Answer

Rbinnun · Answer 1 · 2021-11-07T12:24:51+0000

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.

Explanation:

The (1 - α)% confidence interval for population mean μ, when the population standard deviation is not known is:

$CI=\bar x\pm t_(\alpha/2, (n-1))* (s)/(√(n))$

The information provided is:

$\bar x=4.58\\s=1.10\\\alpha =0.10$

Compute the critical value of t for 90% confidence interval and (n - 1) degrees of freedom as follows:

$t_(\alpha/2, (n-1))=t_(0.10/2, (50-1))=t_(0.05, 49)=1.671$

*Use a t-table for the probability.

Compute the 90% confidence interval for population mean μ as follows:

$CI=\bar x\pm t_(\alpha/2, (n-1))* (s)/(√(n))$

$=4.58\pm 1.671* (1.10)/(√(50))\\=4.58\pm 0.26\\=(4.32, 4.84)$

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:

Hₐ: The mean time it takes to complete a bachelor’s degree is 4 years, i.e. μ = 4.

Hₐ: The mean time it takes to complete a bachelor’s degree is different from 4 years, i.e. μ ≠ 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. μ = 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.

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