Chapter 10.1, Problem 25E

Online testing: Do you prefer taking tests on paper or online? A college instructor gave identical tests to two randomly sampled groups of 35 students. One group took the test on paper and the other took it online. Following are the test scores.

1. Construct a 95% confidence interval for the difference in mean scores between paper and online tests.
2. The instructor claims that the mean scores are the same for both the paper and the online versions of the test. Does the confidence Interval contradict this claim?

To determine

To find: The $95\%$ confidence interval for the difference in mean scores between paper and online test.

Answer to Problem 25E

The $95\%$ confidence interval for the difference in mean scores between paper and online test is $\left(-7.91,2.08\right)$ .

Explanation of Solution

Given information:

The data is,

Paper
79	75	49	78	73	81	70
63	79	65	60	74	64	64
74	69	57	65	61	58	92
71	69	66	71	68	67	81
78	80	76	67	49	56	45

Online
79	75	71	81	56	72	49
75	63	81	74	72	71	73
83	59	78	65	53	47	63
82	81	76	65	82	78	76
65	72	85	84	81	so	79

Concept used:

Minitab is used.

Calculation:

The steps for the confidence interval are,

Import the data, select start and choose the basic statistics option then select the 2 sample t and enter summarized data.

Click option button choose confidence level, test difference and alternative hypothesis and then click ok.

The data is shown below.

  

Figure-1

Therefore, the $95\%$ confidence interval for the difference in mean scores between paper and online test is $\left(-7.91,2.08\right)$ .

To determine

To find: Whether the confident interval contradict the claim.

Answer to Problem 25E

The confident interval does not contradict the claim

Explanation of Solution

Given information:

The data is,

Paper
79	75	49	78	73	81	70
63	79	65	60	74	64	64
74	69	57	65	61	58	92
71	69	66	71	68	67	81
78	80	76	67	49	56	45

Online
79	75	71	81	56	72	49
75	63	81	74	72	71	73
83	59	78	65	53	47	63
82	81	76	65	82	78	76
65	72	85	84	81	so	79

Concept used:

Minitab is used.

Calculation:

Since, the $95\%$ confidence interval for the difference in mean scores between paper and online test is $\left(-7.91,2.08\right)$ and it include $0$ .

Therefore, the confident interval does not contradict the claim.