Question

Womens Heights	Mens Heights
5.8	5.9
5.6	6.0
5.3	5.9
5.6	6.0
5.7	6.4
5.4	6.1
5.0	6.0
5.3	6.1
5.5	5.4
5.3	5.9
6.2	6.1
5.8	5.9
5.3	5.4
5.5	5.5
5.9	6.3
5.3	5.3
5.5	5.3
5.1	5.6
4.6	5.8
6.1	5.8
5.4	5.5
5.0	5.2
4.9	5.9
5.9	6.8
5.3	5.9

	Women’s Heights	Men’s Heights
Sample Mean	5.452	5.84
5% Trimmed Mean	5.4565	5.826
Median	5.4	5.9
Range	.5
IQR (Interquartile Range)	.4	.5
Sample Variance	.14343	.1425
Sample Standard Deviation		.37749

PART 1

The height of women on the basketball team is argued to be 5.5 feet tall. Test the data set of Women’s heights and determine if there is a statistically significant difference between the data set and the test value of 5.5. Perform a 2-sided test and use a significance level of 0.05. State your hypotheses Ho and Ha, the test statistic, the p-value and your conclusion. Also, based on your conclusion, what type of error (Type I or Type II) might have you committed? What is the probability associated with the type of error you chose?

PART 2

The height of men on the basketball team is argued to be 6.1 feet tall. Test the data set of Men’s heights and determine if there is a statistically significant difference between the data set and the test value of 6.1. Perform a 2-sided test and use a significance level of 0.05. State your hypotheses Ho and Ha, the test statistic, the p-value and your conclusion. Also, based on your conclusion, what type of error (Type I or Type II) might have you committed? What is the probability associated with the type of error you chose?

PART 3

Calculate 95% confidence intervals for the true mean height of Women and true men height of Men. Interpret your confidence intervals. Do they overlap. Based on whether the confidence intervals overlap or not, what does this say about whether the true mean height of men could equal the true mean height of women?

Answer 1

REMARK: In part1 and part2 the Alternative Hypothesis Ha is

Ha: There is statistically significant difference between the data set.

In Part1 we Accepted Ho there we committed NO error. Because We accepted the Ho when the Ho is true.

where as in Part2 We rejected Ho here we committed Type I error i.e We Rejected Ho though the Ho is True.

In Part3 We computed the Confidence Intervals for Women Height and Men Height. By comparing those two Confidence Intervals i.e equation I and II ( See the Page # 8) those confidence intervals were not overlapped.