Question

Historically, the time spent by DCSI3710 students on trying to certify any HLS homework is known to have a mean of 35 minutes. In order to examine the claim that homework 12.2 was actually more time consuming, an instructor asked 16 students how much time they spent on it.

1. What is the Null hypothesis for this problem?

2. The 16 students had a mean completion time of 39 minutes and the sample standard deviation was 10 minutes. What is the calculated value of the test statistic in this case?

3. Assume that the p-value associated with the test statistic is 0.08. At a significance level of 0.1, what is the conclusion of the hypothesis test?

Answer 1

(1) Null Hypothesis,
`H_0` :
`\mu` <= 35 minutes

(2) Calculated value of the test statistic is 1.6

(3) We conclude that homework was actually more time consuming

Explanation:

We are given that the time spent by DCSI3710 students on trying to certify any HLS homework is known to have a mean of 35 minutes.

(1) Null Hypothesis,
`H_0` :
`\mu` <= 35 minutes {means that the homework takes less than or equal to 35 minutes}

Alternate Hypothesis,
`H_1` :
`\mu` > 35 minutes {means that the homework was actually more time consuming as it takes more than 35 minutes}

(2) We are provided that the sample of 16 students had a mean completion time of 39 minutes and the sample standard deviation was 10 minutes.

So, the test statistics used here will be;

T.S. =
`(Xbar-\mu)/((s)/(√(n) ) )` ~
`t_n_-_1`

where, X bar = sample mean = 39 minutes

s = sample standard deviation = 10 minutes

n = sample of students = 16

So, test statistics =
`(39-35)/((10)/(√(16) ) )` ~
`t_1_5`

= 1.6

So, calculated value of the test statistic in this case is 1.6 .

(3) We are given that p-value associated with the test statistic is 0.08 or 8% . And the significance level is given as 0.1 or 10%.

It is stated that If p-value is less than significance level ⇒ Reject
`H_0`

If p-value is more than significance level ⇒ Do not Reject
`H_0`

Since here, p-value is less than the significance level as 8% < 10% so we conclude that null hypothesis must be rejected.

Therefore, we conclude that homework was actually more time consuming.