Question

1. Do you prefer taking test on paper or online? An college instructor believes the tests scores will be the same, on average. This 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. The results are below. Test whether the test scores are the same at significance level 0.10. Your complete solution should include a comparative boxplot displaying a box for each group, over the same scale.

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	50	79

Answer 1

Here is the data:

The provided sample means are shown below:

Also, the provided sample standard deviations are:

and the sample sizes are

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: ​

Ha:

This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.10, and the degrees of freedom are df=68.

Hence, it is found that the critical value for this two-tailed test is tc​=1.668, for α=0.10 and df=68.

The rejection region for this two-tailed test is R={t:∣t∣>1.668}.

(3) Test Statistics

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that ∣t∣=1.166≤tc​=1.668, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.2479, and since p=0.2479≥0.10, it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ1​ is different than μ2​, at the 0.10 significance level.

Confidence Interval

The 90% confidence interval is −7.084<μ1​−μ2​<1.255.

Graphically

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