Question

Question 5

A government department is investigating whether the font style used on a website changes the speed at which people read information. A sample of eight randomly selected participants are shown two website pages. The first website uses an Arial font style. The second uses a Verdana font style. The two pages have different text but contain the same number of words.

The table below shows the length of time that each participant took to read the paragraph of text on each page.

Table: Time taken (in seconds) to read website text

Person	A	B	C	D	E	F	G	H
Arial Font	120	85	91	70	130	95	66	94
Verdana Font	115	88	73	59	122	84	70	80

Part a)

Use a paired t-test at the 5% significance level to test whether changing the font style has affected the time taken to read the paragraphs of text.

[9 marks]

Part b)

Briefly explain why this type of test is appropriate for this scenario and this data

[2 marks]

Part c)

If the researcher wanted to use a two sample t-test for independent samples rather than a paired t-test, briefly describe the alterations the researcher would need to make to the data collection process.

[3 marks]

Answer 1

Part a)

Use a paired t-test at the 5% significance level to test whether changing the font style has affected the time taken to read the paragraphs of text.

The following table is obtained:

	Sample 1	Sample 2	Difference = Sample 1 - Sample 2
	120	115	5
	85	88	-3
	91	73	18
	70	59	11
	130	122	8
	95	84	11
	66	70	-4
	94	80	14
Average	93.875	86.375	7.5
St. Dev.	22.113	21.824	7.801
n	8	8	8

and the sample size is n = 8. For the score differences we have

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μD​ = 0

Ha: μD​ ≠ 0

This corresponds to a two-tailed test, for which a t-test for two paired samples be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df = 7

Hence, it is found that the critical value for this two-tailed test is t_c = 2.365 , for α=0.05 and df = 7

(3) Test Statistics

The t-statistic is computed as shown in the following formula:

(4) Decision about the null hypothesis

Since it is observed that |t| = 2.719 >tc​=2.365, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0.0298, and since p = 0.0298<0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean μ1​ is different than μ2​, at the 0.05 significance level.

Part b)

Briefly explain why this type of test is appropriate for this scenario and this data

Since, the data is paired or dependent, one observation is taken twice with both the fonts hence, the paired t test is apt here.

Part c)

If the researcher wanted to use a two sample t-test for independent samples rather than a paired t-test, briefly describe the alterations the researcher would need to make to the data collection process.

Instead of taking observation for one person twice he will have to take the observation independent of each other. As in sampel in both font and not based on whether they survyed before or not