In: Statistics and Probability
Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis.
The principal of a middle school claims that the mean test score of the seventh-graders at his school is higher than 72.1. You wish to test this claim at the 0.05 level of significance. The mean score for a random sample of 101 seventh-graders is 75.7 with a standard deviation of s = 15.2. What criterion would be used for rejecting the null hypothesis, that µ ≤ 72.1?
Group of answer choices
Reject H0 if test statistic > 1.660.
Reject H0 if test statistic > 1.96.
Reject H0 if test statistic > 1.645 or < -1.645.
Reject H0 if test statistic > 1.645.
Here in this scenario The principal of a middle school claims that the mean test score of the seventh-graders at his school is higher than 72.1.
To test this claim we have to use t distribution i.e one sample t test because here the population standard deviations is unknown. According to central limit theorem as sample size is large enough you can use z distribution instead of t both will gives us approximately same result.
Here we are using t distribution based on given sample information and claim the right tailed test will be used as below at 0.05 level of significance as below,
The t critical value is calculated using t table or using Excel at 100 degrees of freedom.
The Rejection region is,
A) Reject H0 if test statistic > 1.660.
Thank you.