question 9 The following table shows the weights (in pounds) and the number of h
ID: 3155083 • Letter: Q
Question
question 9
The following table shows the weights (in pounds) and the number of hours slept in a day by a random sample of infants. Test the claim that
M 0. Use =0.10.1.
Then interpret the results in the context of the problem. If convenient, use technology to solve the problem.
Weight, x
8.1
10.2
9.9
7.2
6.8
11.3
10.9
15.1
Hours slept, y
14.9
14.6
14.1
14.2
13.8
13.2
13.9
12.4
Identify the null and alternative hypotheses.
C.
H0: M =0
Ha M0
Calculate the test statistic.
round to three decimal places as needed.
t =?????
Weight, x
8.1
10.2
9.9
7.2
6.8
11.3
10.9
15.1
Hours slept, y
14.9
14.6
14.1
14.2
13.8
13.2
13.9
12.4
Explanation / Answer
Compute Pearson correlation coefficient, r=-0.734 (using technology). Virtually any technology can find the value of r, here Minitab is used. For which enter the given data>Go to stat> Basic statistics>Correlation>enter C1 and C2 and click OK.
Compute t test statistic.
t=r/sqrt[1-r^2/n-2]
=-0.734/sqrt[1-0.734^2/8-2]
=-2.65
The p value at df=6 (n-2) is 0.0380.
The p value is less than alpha=0.1. Reject null hypothesis to conclude that weight and hours of sleep are negatively linearly correlated.
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