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Random samples of resting heart rates are taken from two groups.Population 1 exercises regularly, and population 2 does not. Thedata from these two samples (in beats per minute) are givenbelow:
Exercise group (sample from population 1): 62.4, 64.1, 66.8,60.7, 68.2, 69.2, 64.9, 70.9, 67.7, 68, 58.5, 58.9, 64.7
No exercise group (sample from population 2): 79.3, 73.8, 75.3,74.7, 76.9, 74.9, 73.2, 75.7, 75.2, 76.7, 78.7
Estimate the difference in mean resting heart rates between thetwo groups using a 9797% confidence interval.
Using a complete test of hypothesis at an ?=0.03?=0.03 level ofsignificance, is there evidence to conclude that those who exerciseregularly have lower resting heart rates?
Use the approximate value for the degrees of freedom (thesmallest between ?1 ? 1 and ?2 ? 1).
(a) Create two vectors to store the data. Find, store anddisplay the mean, standard deviation and number of observations foreach sample.
(b) Draw a properly labelled boxplot for each sample. Comment onthe validity of the assumption of normality for these data.
(c) Construct a confidence interval for the difference in meanresting heart rates between the two groups. Assume normality, anduse the level of confidence given to you in WW. Does the confidenceinterval support a difference between the two means? Explain.
(d) Test the claim that those who exercise regularly have lowerresting heart rates than those who do not. Use the level ofsignificance given to you in WW. You must include: i) null andalternative hypotheses; ii) test statistic; iii) P-value; iv)decision in term of the null hypothesis; v) decision incontext.
(e) Create a properly labelled plot that includes the samplingdistribution of the statistic under the null hypothesis, the valueof the statistic as a vertical line, and the P-value.
