Question

A researcher is interested in determining whether the illumination level in a room affects how quickly clients can be put into a trance. The time (in seconds) it took for five clients to go into a trance when it was done in a room that was lit with low light was measured, as was the time it took for the same clients to go into a trance in a brightly lit room. The theory being tested does not predict which light condition will lead to going into a trance more quickly. The data are given below:

Low Light	Bright Light
45	49
15	13
75	82
30	30
57	60

what is the mD? SSD? est. ?D=? est. ?MD=?t=?

Answer 1

Md= -2.4

Standarad deviation of difference=3.507

Since level of significance yo have mentioned therefore we wil use alpha=0.05

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: \mu_DμD​ = 0

Ha: \mu_DμD​ ≠ 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=4.

Hence, it is found that the critical value for this two-tailed test is tc​=2.776, for α=0.05 and df=4.

The rejection region for this two-tailed test is R={t:∣t∣>2.776}.

(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∣=1.53≤tc​=2.776, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.2007, and since p = 0.2007 \ge 0.05p=0.2007≥0.05, 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 0.05 significance level. Threrefore we can conclude that the illumination level in a room doesnot affects how quickly clients can be put into a trance.

Confidence Interval The 95% confidence interval is −6.755<μD​<1.955.