Question

Test the claim that for the population of statistics final exams, the mean score is 78 using alternative hypothesis that the mean score is different from 78. Sample statistics include n=27,x¯=79, and s=16. Use a significance level of α=0.05. (Assume normally distributed population.)

The test statistic is ____
The positive critical value is _____
The negative critical value is _____
The conclusion is ____

Answer 1

Answer)

Null hypothesis Ho : u = 78

Alternate hypothesis Ha : u not equal to 78

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

t = (79 - 78)/(16/√27) = 0.325

As the population standard deviation is unknown here and we are given with sample s.d as the best estimate, we will use t distribution table to conduct the test.

Degrees of freedom is = n-1 = 26

For 26 dof and 0.05 alpha

Critical values are -2.056 and 2.056.

Negative critical value = -2.056.

Positive critical value = 2.056

Rejection region is reject Ho if test statistics is less than -2.056 or greater than 2.056.

Conclusion :

Since 0.325 is not greater than 2.056

We fail to reject the null hypothesis Ho.