Question

A computer professor is interested in studying the amount of time it would take students enrolled in the Introduction to Computers course to write and run a program in Matlab. The professor hires you to analyze the following results in minutes from a random sample of 9 students:
10 12 8 16 12 13 10 11 15

Required:
At the 0.05 level of significance, is there evidence that the population average time is greater than 10 minutes?

Answer 1

Answer:

Following are the solution to the given question:

Step-by-step explanation:

In this question, firstly we calculating the $\bar{x} \ \ and \ \ s$

$\bar{x}=11.89 \\\\s = 2.52\\\\n = 9\\\\\alpha=0.05$

$H_0 : u \leq 10\\\\ H_1 : u > 10$

It is an upper test  and testing the statistics:

$t=\frac{\bar{x}-\mu }{\frac{s}{\sqrt{n}}}\\\\t=\frac{11.89-10 }{\frac{2.52}{\sqrt{9}}}\\\\t=2.25$

So, the test statistics $t=2.25$

$\alpha=0.05 \\\\ d.f = n-1$

     $=9-1\\\\=8$

critical value =2.306 ( using t-table ) $critical\ value >\ test\ statistics , \ Fail\ to\ Reject\ H_0$

Decision: We should not reject the null hypothesis.