Question

DATA: The following data are collected from virtual people living on an Island showing the systolic and diastolic blood pressure (measured in mmHg) for 30 men and 30 women.

Serial number	Male	Systolic	Diastolic	Female	Systolic	Diastolic
1	M	157.8	91.0	F	157.4	90.3
2	M	160.5	90.7	F	154.8	89.4
3	M	157.5	88.1	F	155.4	91.8
4	M	169.4	94.3	F	168.4	94.2
5	M	160.1	90.2	F	163.0	90.5
6	M	160.5	92.9	F	158.2	90.8
7	M	147.5	87.9	F	104.3	61.5
8	M	156.5	90.2	F	99.8	64.6
9	M	154.9	89.2	F	102.4	65.2
10	M	153.7	91.0	F	114.2	76.5
11	M	170.4	94.9	F	94.1	58.7
12	M	163.0	90.3	F	101.7	66.6
13	M	158.2	90.7	F	108.7	61.8
14	M	157.5	91.1	F	104.6	41.2
15	M	160.2	90.7	F	123.4	72.3
16	M	155.8	87.7	F	93.5	61.1
17	M	166.7	93.4	F	89.6	56.1
18	M	159.1	90.0	F	112.8	62.2
19	M	160.3	93.1	F	107.2	48.3
20	M	150.3	87.8	F	116.1	62.1
21	M	112.3	70.6	F	181.3	102.5
22	M	125.5	89.7	F	100.0	61.7
23	M	115.6	65.4	F	127.0	53.8
24	M	136.2	90.5	F	107.5	74.9
25	M	143.3	97.1	F	116.3	67.0
26	M	116.7	64.7	F	97.8	71.1
27	M	123.9	78.9	F	155.7	64.1
28	M	124.8	69.0	F	106.6	85.8
29	M	131.9	87.2	F	110.4	59.6
30	M	153.9	95.2	F	105.0	70.3

Question: Are the population means of systolic blood pressure for men and women living on the island are different?

State the question. (1 point)

Make a suitable plot to compare the systolic blood pressure for men and women and interpret the plot. (2 points)

Define the parameters and state the hypotheses. (3 points)

State and check the assumptions for the significance test for the difference of population means. Make sure to explain why the assumptions are met or not. (Hint: A check mark is not sufficient.) (2 points)

State the test statistic and the p-value. Include the output from the statistical software package. (2 points)

Interpret the p-value and make a conclusion. (2 points)

State and check the assumptions for the 95% confidence interval for the difference of population means. Make sure to explain why the assumptions are met or not. (Hint: A check mark is not sufficient.) (2 points)

State the confidence interval for the difference of population means. Include the output from the statistical software package. (2 points)

Interpret the confidence interval. (2 points)

Conclusion: Suppose that you are a journalist that has been asked to summarize the results of this study. Give a brief summary of the results so that a friend who is not taking a statistics course would understand it. (2 points)

Answer 1

• To Test that the systolic blood pressure of male and female is different .
• 
• 
• From the above graph we can see that male systolic blood pressure is positively skewed and for female it is negatively skewed.
• The blood pressure for Male is on the higher side and for females it is on the lower side.
• Hence we can see from the above graphs the systolic blood pressure for male and female are different.
• Let X1 be the random variable denoting the systolic blood pressure for male
• Let X2 be the random variable denoting the systolic blood pressure for females
• ASSUMPTION
• The Central Limit Theorem justifies the use of a normal approximation
  for the distribution of the test statistic in sampling from any reasonable
  populations, so the requirement that we are sampling from normal distributions
  is not necessary when we have large samples.
• HYPOTHESIS
• Let null hypothesis denote that the systolic blood pressure for male and female is equal
• and let the alternate hypothesis denote that the systolic blood pressure for male and female is not equal
  
• H0: vs H1:
• The test statistics is given by
• 
• The mean of male and female systolic blood pressure is
• =148.8 and=121.24
• The standard deviation is given by for male==17.00037
• for female==26.48725
• where the pooled variance for equal variances is given by
• sp²==482.5
• sp=sqrt(482.5)=21.96
• by substituting the above values the test statistics is given by 4.8593
• The r code to find the p value is given
• p value=2*pt(t test, lenght(df-1),lower=FALSE)
• pt is used for two sided test
• therefore=2*pt(4.859,58,lower=FALSE)
• =9.338*e^-06
• The p value obtained is less than 5% significant value .
• Therefore we do have enough evidence t reject null hypothesis.
• Therefore we conclude the mean of systoloic blood pressure for male and female is different.