Question

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: a) there is sufficient sample evidence for the program’s claim to be considered correct. b) there is insufficient sample evidence for the program’s claim to be considered correct. c) there is insufficient sample evidence for the program’s claim to be considered incorrect. d) there is sufficient sample evidence for the program’s claim to be considered incorrect.

Answer 1

• EXPLANATION.
• The actual decision is based on the value of a suitable function of the data, the test statistic.
• The set of possible values of the test statistic itself divides into two subsets, a region in which the value of the test statistic is consistent with H0, and its complement, the critical region (or rejection region), in which the value of the test statistic is inconsistent with H0.
• If the test statistic has a value in the critical region, H0 is rejected.
• The test statistic must be such that its distribution is completely specified when the value of the parameter itself is specified (and in particular “under H0” ie when H0 is true).
• ANSWER
• HYPOTHESIS TO BE TESTED.
• Let the null hypothesis be that the students graduate in 4 years on average.
• vs
• Alternate hypothesis be that the students graduate in less than 4 years on average.
• CONCLUSION
• In the above example the test satistics obtainesd is -1.69.
• The critical value at 5% significant level of normal distribution is 1.645.
• The test statistics obatined lies outside the upper and lower critical value of 1.645
• Hence we have enough evidence to reject the null hypothesis.
• Hence we conclude that their students graduate in less than 4 years on average.