Question

Do female college students tend to weigh more or less than male college students, on average? Suppose that we use data from the Student Data sheet to help us make a decision about this question. We will assume that those who responded to the student data sheet are representative of all college students and are a random sample. Below are summary statistics from the student data sheet (rounded to the nearest integer):

Sex?	N	Mean	St. Dev	Median	Minimum	Maximum
Female	96	150	44	140	62	250
Male	94	189	42	184	95	350
Total	190	169	47	165	62	350

a. Create a 95% confidence interval for the mean weight of all female college students

b. interpret the interval created in part a

c. create a 95% confidence interval for the mean weight of all male college students

d. interpret the interval created in part c

e. based on your interpretations of the confidence intervals above, do these data support any difference in average weight between female and male college students? Breifly justify your response.

Answer 1

Solution:

Part a

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

n = 96

df = n – 1 = 96 – 1 = 95

Confidence level = 95%

Critical t value = 1.9853

(by using t-table)

Xbar = 150

S = 44

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 150 ± 1.9853*44/sqrt(96)

Confidence interval = 150 ± 8.9152

Lower limit = 150 - 8.9152 = 141.0848

Upper limit = 150 + 8.9152 = 158.9152

Part b

We are 95% confident that the population mean weight of all female college students will lies between 141.08 and 158.92.

Part c

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

n = 94

df = n – 1 = 94 – 1 = 93

Confidence level = 95%

Critical t value = 1.9858

(by using t-table)

Xbar = 189

S = 42

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 189 ± 1.9858*42/sqrt(94)

Confidence interval = 189 ± 8.6024

Lower limit = 189 - 8.6024 = 180.3976

Upper limit = 189 + 8.6024 = 197.6024

Part d

We are 95% confident that the population mean weight of all male college students will lies between 180.40 and 197.60.

Part e

Yes, from the above two confidence intervals, it is observed that the average weight of male students is greater than the average weights of female students because the confidence interval of male have the lower limit greater than upper limit of confidence interval for female students. Also, there is no any overlapping observed in these two intervals.