Question

Ross has created a puzzle game that he believes will take 30 minutes for a player to complete. A week after the game's release, he collects data for a random sample of 20 players on how long they took to complete the game. These times, in minutes, are shown in the following table.

Use Excel to test whether the mean time to complete the game is different from 30 minutes, and then draw a conclusion in the context of the problem. Use α=0.05.

Time (minutes)
32
33
31
21
30
27
41
33
27
37
38
34
27
40
28
33
26
27
40
40

Select the correct answer below:

1. Reject the null hypothesis. There is sufficient evidence to conclude that the mean is not equal to 30 minutes.

2. Reject the null hypothesis. There is insufficient evidence to conclude that the mean is not equal to 30 minutes.

3. Fail to reject the null hypothesis. There is sufficient evidence to conclude that the mean is not equal to 30 minutes.

4. Fail to reject the null hypothesis. There is insufficient evidence to conclude that the mean is not equal to 30 minutes.

Answer 1

Given:

X : Time for complete the game (in minutes)

To test whether the mean time to complete the game is different from 30 minutes.

Ho: µ = 30 vs H1: µ ≠ 30

Excel Output:-

t-Test: One-Sample
	Time
Mean	32.25
Variance	32.51315789
Observations	20
Hypothesized Mean	30
df	19
t Stat	1.764688028
P(T<=t) one-tail	0.046843105
t Critical one-tail	1.729132812
P(T<=t) two-tail	0.093686211
t Critical two-tail	2.093024054

test statistic = 1.7647

Critical Value = 2.0930

p-value = 0.0937

Here, test statistic = 1.7647 < Critical Value = 2.0930

OR

p-value = 0.0937 > α = 0.05

Therefore we Fail to reject the null hypothesis.

Conclusion:

Fail to reject the null hypothesis. There is insufficient evidence to conclude that the mean is not equal to 30 minutes.