A business school finds that the average number of years of work experience of MBA applications is at least 3 years. Based on last year's applicants, it was found that among a sample of 47, the average number of years of work experience is 2.57 with a standard deviation of 3.67. What conclusion can the school reach? g

The school will reach a conclusion that the average number of years of work experience of MBA applications is at least 3 years

Step-by-step explanation: This question did not choose a level of significance (α) and that's one of the most important thing to make decisions, so therefore, for this test, I assume a level of significance of 5%.

I am also assuming that the distribution of the data set is of a normal distribution.

Null hypothesis is that the average MBA application is of at least 3 years work experience.

H": u≥3 where H" = null hypothesis.

After taking a sample of 47 students, it was noticed that the average number of work years experience is 2.57 years.

2.57 is a value lesser than 3, hence we have the alternative hypothesis as

H' : u < 3

Because of the direction of the alternative, we conclude that the test is lower tailed.

Hence population mean (u) =3, sample mean (x) = 2.37

Sample size (n)= 47 and population standard deviation (σ) = 3.67.

Since population standard deviation is known, and sample size is greater than 30 (47), the z test is used in getting the value of our test statistics

Z = x - u/(σ/√n)

Z = 2.57 - 3/(3.67/√47)

Z = - 0.42/0.5353

Z = - 0.78

Above is our z score.

Initially we said our test is lower tailed (because the value of the alternative hypothesis is lesser than the null), hence our critical value will be positioned on the negative axis of the normal distribution

For a lower tailed z test, the critical value is - 1.645.

With area left of the critical value as the rejection region (that's values lesser than - 1.645) and area right of the critical value as the acceptance region ( that's values greater than - 1.645).

Let us now compare our z score to the critical value.

Our z score is - 0.78 and our critical value is - 1.645, it is glaring that our z score is lesser than the critical value hence making it fall in the acceptance region

Since we are in the acceptance region, we will accept the initial claim by the school ( null hypothesis)

Attached to this answer is a graphical representation of how I made my decision for better comprehension.

The school will reach a conclusion that the average number of years of work experience of MBA applications is at least 3 years at a 5% level of significance