Question

A computer company that recently introduced a new software product claims that the mean time it takes to learn how to use this software is not more than 2 hours for people who are somewhat familiar with computers. A random sample of 12 such persons was selected. The following data give the times take by these persons to learn the software.

1.75 2.25 2.40 1.9 1.5 2.75 2.15 2.25 1.8 2.20 3.25 2.60

Test at the 1% significance level whether company’s claim is true. Assume that the times by all persons who are somewhat familiar with computers to learn how to use this software are approximately normally distributed.

Answer 1

Since the claim is that the time taken to learn the software is not more than which means at most 2 hours, this is a right tailed test.

From the data: = 2.23, s = 0.353, n = 12

The Hypothesis:

H0: µ < 2

Ha: μ > 2

This is a right tailed Test.

The Test Statistic: Since the population standard deviation is unknown, we use the students t test.

The test statistic is given by the equation:

The p Value:    The p value (Right Tail) for t = 2.26, for degrees of freedom (df) = n-1 = 11, is; p value = 0.0225

The Critical Value:   The critical value (Right Tail) at = 0.01, for df = 11, t critical = +2.72

The Decision Rule:   If t observed is > t critical, then Reject H0

Also if P value is < , Then Reject H0.

The Decision:   Since t observed (2.26) is < t critical (2.72), We Fail to Reject H0.

Also since P value (0.0225) is > (0.01) , We Fail to Reject H0.

The Conclusion: There is isn’t sufficient evidence at the 99% significance level to warrant rejection of the company's claim that the mean time it takes to learn this software is not more than 2 hours.

____________________________________________________

Calculation for the mean and standard deviation:

Mean = Sum of observation / Total Observations

Standard deviation = SQRT(Variance)

Variance = Sum Of Squares (SS) / n - 1, where SS = SUM(X - Mean)².

Sno	x	Mean	(x - Mean )2
1	1.75	2.23	0.2336
2	2.25	2.23	0.0003
3	2.4	2.23	0.0278
4	1.9	2.23	0.1111
5	1.5	2.23	0.5378
6	2.75	2.23	0.2669
7	2.15	2.23	0.0069
8	2.25	2.23	0.0003
9	1.8	2.23	0.1878
10	2.2	2.23	0.0011
11	3.25	2.23	1.0336
12	2.6	2.23	0.1344
Total	26.8	SS	1.3736
Mean	2.23	Variance	0.1249
		SD	0.353