A physiologist wants to determine whether a particular running programme decreas
ID: 3333765 • Letter: A
Question
A physiologist wants to determine whether a particular running programme decreases resting heart rate of adults who can already comfortably run for 5 kilometres.The running programme is a one year programme where participants are asked to follow a series of simple extensions to their current running sessions.A random sample of 35 people who can already comfortably run for 5 kilometres was selected. The heart rates (beats per minute) of these people were measured before they started the running programme (Pulse1) and then again at the conclusion of the running programme (Pulse2).
You are asked to carry out a hypothesis test to see if there is statistically significant evidence that the running programme has had an effect on the resting heart rate.
a)Explain why a paired test rather than a two-sample t-test is the appropriate test to analyse this data.
b)Is a one or a two-sided test appropriate for this situation? Explain
c)State the null and alternative hypotheses for this test in words and/or symbols
d)Use Minitab Express to carry out the paired test to determine whether evidence from the study suggests that the running programme has decreased the resting heart rate
e)Show how the value of the test statistic is calculated by hand.
f)What is the degrees of freedom for the test and the critical value for a significance level of = 0.05?
g)Is there evidence to reject the null hypothesis? Explain.
h)State the assumption(s) needed for this test to be valid.
j)Construct a 95% confidence interval for the mean difference (pulse1 – pulse2)
k)Interpret this confidence interval in context.
l)What effect did the running programme have on the resting heart rate? State your conclusion in context.
Pulse1 Pulse2 73 56 55 50 61 54 63 58 65 56 69 66 69 76 57 60 60 54 103 68 79 82 81 72 69 84 61 60 61 52 43 54 67 58 57 62 61 60 65 64 91 62 61 66 87 58 79 62 125 88 85 54 89 70 85 74 100 92 97 60 101 88 103 70 95 80 83 54 113 72Explanation / Answer
a. There are data of heart rate for 35 people before and after the program, thus the data are paired. Therefore, paired t test is appropriate than two-samples t test.
b. The tentative proposition states that running program has an effect on resting heart rate. Thus, pulse 2 is expected to be lower than pulse 1. Since, direction is specified, it is one-sided test.
c. H0:mud=0 (running program has no effect on resting heart rate)
H1:mud>0 (running program has an effect on resting heart rate)
d=before-after
d. Enter data in Minitab-Stat-Basic statistics-Paired t-select Each sample in a column-enetr C1 and C2 corresponding to Sample1 and Sample2-click Options and select Difference>hypothesized difference-click OK twice. The session window dispaly the output.
The t value is 4.68, p value is:0.000
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