6.A psychology professor of a large class became curious as to whether the students who turned in t

Hi brendalee

Null hypothesis: Mean test score for students who turned in the test first = overall test mean

Alternative hypothesis: Mean test score for students who turned in the test first ≠ overall test mean

Significance level: .05

Test statistic / critical value: t-value of 1.96 (note that this critical value is given for a sample of infinite size. Because n of the overall sample has not been provided, t cannot be precisely calculated)

Conclusion: Reject the null hypothesis if the |t| of the comparison between the two means < 1.96

Confidence limits for the 95% confidence interval

Assuming n = 100, the 95% confidence interval is given by the formula of 75 ± (2.04)(1.8) = 71.33 to 78.67

[Note that the 95% confidence interval for the entire sample cannot be perfectly estimated because n is not given, and the 95% confidence interval for the students who turned in their test first cannot be calculated because the standard deviation for this sample has not been given].

The provided sample mean is 78, and the known population standard deviation is σ=10, and the sample size is n = 20

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ  = 75

Ha: μ≠75

This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=.05, and the critical value for a two-tailed test is z = 1.96

The rejection region for this two-tailed test is R={z:∣z∣>1.96}

(3) Test Statistics

The z-statistic is computed as follows:

z = 1.342

(4) Decision about the null hypothesis

Since it is observed that ∣z∣=1.342≤z =1.96 , it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p = 0.1797, and since p=0.1797≥.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

μ is different than 75, at the .05 significance level.

Confidence Interval

The 95% confidence interval is given as 73.617<μ<82.383.

In this post, https://biology-forums.com/index.php?topic=139802.0, A and D are answered and accepted as best answer too!