Question

The Bay Area Online Institute (BAOI) has set a guideline of 60 hours for the time it should take to complete an independent study course. To see if the guideline needs to be changed and if the actual time taken to complete the course exceeds60 hours, 16 students are randomly chosen and the average time to complete the course was 68hours with a standard deviation of 20 hours. What inference can BAOI make about the time it takes to complete this course?

Answer 1

At the 5% level, BAOI can infer that the average time to complete does not exceeds 60 hours.

Explanation:

From the question we are told that

The population mean is
`\mu = 60 \ hr`

The sample size is
`n = 16`

The sample mean is
`\= x = 68 \ hr`

The standard deviation is
`\sigma = 20 \ hr`

The null hypothesis is
`H_o : \mu = 60`

The alternative
`H_a : \mu > 60`

Here we would assume the level of significance of this test to be

`\alpha = 5\% = 0.05`

Next we will obtain the critical value of the level of significance from the normal distribution table, the value is
`Z_(0.05) = 1.645`

Generally the test statistics is mathematically represented as

`t = ( \= x - \mu)/( ( \sigma )/(√(n) ) )`

substituting values

`t = ( 68 - 60 )/( ( 20 )/(√(16) ) )`

`t = 1.6`

Looking at the value of t and
`Z_(\alpha )` we see that
`t< Z_(\alpha )` hence we fail to reject the null hypothesis

This means that there no sufficient evidence to conclude that it takes more than 60 hours to complete the course

So

At the 5% level, BAOI can infer that the average time to complete does not exceeds 60 hours.