Lesson 13: Inference for Two Means (Independent Samples)

Solutions

Problem	Part	Solution
1	-	There is no pairing between the two groups. Group 1 does not determine Group 2.
2	-
3	A	Is there a difference between the mean wages of BYU-Idaho male students and female students?
3	B	$H_o: \mu_1 = \mu_2$ $H_a: \mu_1 \neq \mu_2$
4	-	Students from one of the Math Department professor’s classes took a survey which asked how much they make as an hourly wage.
5	-	-Males: $\bar{x} =11.935$, $s=10.491$, $n=85$ - Females: $\bar{x}=9.759$, $s=3.169$, $n=91$ - You should also include two histograms here, one for the men and one for the women.
6	A	Independent Samples Hypothesis test
6	B	-The sample size is large for each sample so we can assume normality. - It was not a simple random sample.
6	C	$t= \pm 1.836$
6	D	$df = 98.263$
6	E	$\text{P-value} = 0.069$, $\alpha = 0.05$, $\text{p-value} > \alpha$
6	F	fail to reject the null hypothesis
6	G	We have insufficient evidence to say that there is a difference between wages of male and female BYU-Idaho students.
6	H	(-0.176, 4.529) or (-4.529, 0.176)
6	I	-We are 95% confident that the true difference in mean wages between women and men at BYU-Idaho is somewhere between $-0.18 and $4.53, or $-4.53 and $0.18. - We can also see that there is insufficient evidence using the confidence interval method because zero is included in our confidence interval.
7		Answers may vary

Problem	Part	Solution
1	-	There is no pairing between the two groups. Group 1 does not determine Group 2.
2	-
3	A	Is there a difference between the mean wages of BYU-Idaho male students and female students?
3	B	\(H_o: \mu_1 = \mu_2\) \(H_a: \mu_1 \neq \mu_2\)
4	-	Students from one of the Math Department professor’s classes took a survey which asked how much they make as an hourly wage.
5	-	-Males: \(\bar{x} =11.935\), \(s=10.491\), \(n=85\) - Females: \(\bar{x}=9.759\), \(s=3.169\), \(n=91\) - You should also include two histograms here, one for the men and one for the women.
6	A	Independent Samples Hypothesis test
6	B	-The sample size is large for each sample so we can assume normality. - It was not a simple random sample.
6	C	\(t= \pm 1.836\)
6	D	\(df = 98.263\)
6	E	\(\text{P-value} = 0.069\), \(\alpha = 0.05\), \(\text{p-value} > \alpha\)
6	F	fail to reject the null hypothesis
6	G	We have insufficient evidence to say that there is a difference between wages of male and female BYU-Idaho students.
6	H	(-0.176, 4.529) or (-4.529, 0.176)
6	I	-We are 95% confident that the true difference in mean wages between women and men at BYU-Idaho is somewhere between $-0.18 and $4.53, or $-4.53 and $0.18. - We can also see that there is insufficient evidence using the confidence interval method because zero is included in our confidence interval.
7		Answers may vary