Question

The data studies the effect of dietary calcium on blood pressure. In the experiment, one group of black male adults received calcium supplements for 12 weeks. A control group of black male adults was given placebos for 12 weeks. Earlier tests indicated that calcium could be more effective in the black population. The data are seated systolic blood pressure at the beginning and end of the 12 weeks measured in mm Hg. The data include the decrease after 12 weeks (a negative value indicates an increase).

If you choose to use the table for calculating the p value range, please also report what you calculated for t (or for F)!!!!!!   Data from Lyle et al., JAMA 257:1772-1776 (1987)

                  Calcium Group

Begin                       End                            Decrease

107                           100                           7

110                           114                           -4

123                           105                           18

129                           112                           17

112                           115                           -3

111                           116                           -5

107                           106                           1

112                           102                           10

136                           125                           11

102                           104                           -2

                  Placebo Group

Begin                       End                            Decrease

123                           124                           -1

109                           97                              12

112                           113                           -1

102                           105                           -3

98                              95                              3

114                           119                           -5

119                           114                           5

112                           114                           -2

110                           121                           -11

117                           118                           -1

130                           133                           -3

1. (4) Treat the two groups (calcium and placebo) as independent samples, equal variances. Look only at the decrease columns (you are now comparing the calcium decrease column to the placebo decrease column). Perform a test to determine the p-value for the decrease. State the null and alternative hypothesis. Calculate a 95% confidence interval for the decrease.

2. (4) Treat the two groups as independent samples, unequal variances. Look only at the decrease columns (calcium vs. placebo). Perform a test to determine the p-value for the decrease. State the null and alternative hypothesis. Calculate a 95% confidence interval for the decrease.

3. (4) Do a two-sided t-test to compare the sample groups. Look at the Begin column for calcium and the Begin column for placebo. Report the p-value. Based on that p-value, do you have any reason to believe that the sample groups were significantly different headed into the experiment?

Answer 1

(a) The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 ≠ µ2

Decrease	Decrease_1
5.00	-0.64	mean
8.74	5.87	std. dev.
10	11	n
	19	df
	5.636	difference (Decrease - Decrease_1)
	54.344	pooled variance
	7.372	pooled std. dev.
	3.221	standard error of difference
	0	hypothesized difference
	1.750	t
	.0963	p-value (two-tailed)
	-1.105	confidence interval 95.% lower
	12.378	confidence interval 95.% upper
	6.742	margin of error

The p-value is 0.0963.

Since the p-value (0.0963) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that there is a decrease.

The 95% confidence interval for the decrease is between -1.105 and 12.378.

(b) The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 ≠ µ2

Decrease	Decrease_1
5.00	-0.64	mean
8.74	5.87	std. dev.
10	11	n
	15	df
	5.636	difference (Decrease - Decrease_1)
	3.283	standard error of difference
	0	hypothesized difference
	1.717	t
	.1066	p-value (two-tailed)
	-1.361	confidence interval 95.% lower
	12.633	confidence interval 95.% upper
	6.997	margin of error

The p-value is 0.1066.

Since the p-value (0.1066) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that there is a decrease.

The 95% confidence interval for the decrease is between -1.361 and 12.633.

(c) The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 ≠ µ2

Begin	Begin_1
114.90	113.27	mean
10.84	9.02	std. dev.
10	11	n
	19	df
	1.627	difference (Begin - Begin_1)
	98.478	pooled variance
	9.924	pooled std. dev.
	4.336	standard error of difference
	0	hypothesized difference
	0.375	t
	.7116	p-value (two-tailed)

The p-value is 0.7116.

Since the p-value (0.7116) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that the sample groups were significantly different.

Please give me a thumbs-up if this helps you out. Thank you!