Question

I want you to conduct a hypothesis test for a difference of means for cholesterol levels between male and female students. There are 148 females and 164 males in our sample. You can treat this as a large sample problem and use z-values for confidence intervals and hypothesis tests (however, Excel uses a t-value in anything it calculates). The output from Microsoft Excel is given below to help. Your job will be to find the right numbers in the output to help solve the problem. EXCEL DESCRIPTIVE STATISTICS FOR CHOLESTEROL LEVELS OF MALES AND FEMALES Cholesterol Females Males Mean 200.318 196.085 Standard Error 0.881 0.966 Median 201 196 Mode 194 196 Standard Deviation 10.721 12.372 Sample Variance 114.939 153.072 Kurtosis -0.493 0.015 Skewness -0.109 0.086 Range 47 61 Minimum 176 166 Maximum 223 227 Sum 29647 32158 Count 148 164 Confidence Level (95.0%) 1.742 1.908 3. The Descriptive Statistics are given above. Put a 95% Confidence Interval around just the male mean. What is the upper bound for the 95% CI? Use 3 significant decimal places and use the proper rules of rounding.

Answer 1

We need 95% confidence interval around male mean.

Using the following table

	Females	Males
Mean	200.318	196.085
Standard Error	0.881	0.966
Median	201	196
Mode	194	196
Standard Deviation	10.721	12.372
Sample Variance	114.939	153.072
Kurtosis	-0.493	0.015
Skewness	-0.109	0.086
Range	47	61
Minimum	176	166
Maximum	223	227
Sum	29647	32158
Count	148	164
Confidence Level(95.0%)	1.742	1.908

We have the following information regarding male

n=164 is the sample size of males

is the sample mean cholesterol level for male students

is the estimated standard error of mean

(Just as a note the above standard error can be estimated using the sample standard deviation as

)

the sample size n=164 is greater than 30. Hence we can use normal distribution as the sampling distribution of mean.

We need to get the critical value of z for 95% confidence interval.

95% confidence interval indicates that the level of significance is . This is the total area under both the tails. The area under the right tail is half of 0.05. The right tail critical value is

Using standard normal table, we get that for z=1.96, P(Z<1.96) = 0.975

Hence,

Now we can get the 95% confidence interval for the average cholesterol level of males

The upper bound is

ans: the upper bound for the 95% CI is 197.978

The lower bound is

ans: the lower bound for the 95% CI is 194.192

Similarly we can find the 95% confidence interval for average female cholesterol levels

n=148 is the sample size of females

is the sample mean cholesterol level for female students

is the estimated standard error of mean

The value of critical value of z remains the same.

The upper bound is

ans: the upper bound for the 95% CI is 202.045

The lower bound is

ans: the lower bound for the 95% CI is 198.591

The 95% CI for average cholesterol level for males is [194.192,197.978] and average cholesterol level for females is [198.591,202.045]

We can see that these confidence intervals do not overlap (The upper bound of males is lower than the lower bound of females). That means we can conclude that at 95% confidence,  means for cholesterol levels between male and female students are different.

,