Question

multiple choice 4 points
21
state your conclusion to the hypothesis test.
a certain academic program claims that their students graduate in less than 4 years on average. a random sample of 50 students is taken
and the mean and standard deviation are found. the test statistic is calculated to be -1.69. using a 5% significance level, the conclusion
would be.
there is sufficient sample evidence for the programs claim to be considered correct.
there is insufficient sample evidence for the programs claim to be considered correct.
there is insufficient sample evidence for the programs claim to be considered incorrect.
there is sufficient sample evidence for the programs claim to be considered incorrect.

Explanation:

Step1: Determine the type of test

Since the claim is about the mean graduation time being less than 4 years, this is a one - tailed (left - tailed) hypothesis test.

Step2: Find the critical value

For a 5% significance level in a left - tailed test, the critical value \(z_{crit}\) is - 1.645 (from the standard normal distribution table).

Step3: Compare the test statistic and the critical value

The test statistic \(z=-1.69\). Since \(-1.69<-1.645\) (the test statistic falls in the rejection region).

Answer:

There is sufficient sample evidence for the program's claim to be considered correct.