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

Following are the solution to the given question:

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 }{(s)/(√(n))}\\\\t=(11.89-10 )/((2.52)/(√(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.