Question

1. A consumer group is testing camp stoves. To test the heating capacity of a stove, they measure the time required to bring 2 quarts of water from 50 degrees to boiling.

Two competing models are under consideration. Thirty-six stoves of each model were tested and the following results were obtained.

    

     Model 1: mean time is 11.4 and standard deviation is2.5

     Model 2: mean time is   9.9 and standard deviation is 3.0

1. Is there any difference between the performances of these two models? {use a .05 level of significance}. Find the p-value of the sample statistic and do a significance test.
2. Find a 95% confidence interval for the difference of the means.

Answer 1

Excel Addon PHStat used

1. A consumer group is testing camp stoves. To test the heating capacity of a stove, they measure the time required to bring 2 quarts of water from 50 degrees to boiling.

Two competing models are under consideration. Thirty-six stoves of each model were tested and the following results were obtained.

    

     Model 1: mean time is 11.4 and standard deviation is2.5

     Model 2: mean time is   9.9 and standard deviation is 3.0

1. Is there any difference between the performances of these two models? {use a .05 level of significance}. Find the p-value of the sample statistic and do a significance test.

Two tailed test

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	36
Sample Mean	11.4
Sample Standard Deviation	2.5
Population 2 Sample
Sample Size	36
Sample Mean	9.9
Sample Standard Deviation	3
Intermediate Calculations
Population 1 Sample Degrees of Freedom	35
Population 2 Sample Degrees of Freedom	35
Total Degrees of Freedom	70
Pooled Variance	7.6250
Standard Error	0.6509
Difference in Sample Means	1.5000
t Test Statistic	2.3047
Two-Tail Test
Lower Critical Value	-1.9944
Upper Critical Value	1.9944
p-Value	0.0242
Reject the null hypothesis

Calculated t = 2.3047, P=0.0242 which is < 0.05 level of significance.

The null hypothesis is rejected.

We conclude that there is a difference between the performances of these two models.

2. Find a 95% confidence interval for the difference of the means.

Confidence Interval Estimate
for the Difference Between Two Means
Data
Confidence Level	95%
Intermediate Calculations
Degrees of Freedom	70
t Value	1.9944
Interval Half Width	1.2981
Confidence Interval
Interval Lower Limit	0.2019
Interval Upper Limit	2.7981

95% CI for mean difference = ( 0.2019, 2.7981)