Questions 1, 2, 3, and 4 use the X and Y data below. You can think of this data as representing the heights of 5 individuals (labelled A,B,C,D,E) at ages 11 (X column) and 12 (Y column). Paired Y-X Obs X A 60 B 61 62 63 64 с D E Y 62 62 63 64 66 The means and variances for X and Y are shown below. (You can verify to practice calculation steps.) X Mean: 62, X Variance: 2.5 | Y Mean: 63.4, Y Variance: 2.8 The Y-X difference column has not been computed. You need to fill this out and compute the corresponding mean and variance (for Y-X) for question 3. Test whether the population mean of Y is no greater than 1/2 (0.5) unit higher than the population mean for X as the null hypothesis (Ho) vs the population mean of Y is more than 1/2 unit greater than the population mean for X as the alternative hypothesis (H1). What is the small sample t statistic for the test of Ho? Round to two decimal places (e.g., 1.23) Assume the measurements are independent (not a paired test), the variances are not equal and the degrees of freedom for the small sample test can be approximated by 5 + 5 -2 = 8.

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Questions 1, 2, 3, and 4 use the X and Y data below. You can think of this data as representing the heights of 5 individuals (labelled A,B,C,D,E) at ages
11 (X column) and 12 (Y column).
Paired Y-X
Obs X
A
B
с
D
E
60
61
62
63
64
Y
62
62
63
64
66
The means and variances for X and Y are shown below. (You can verify to practice calculation steps.)
X Mean: 62, X Variance: 2.5 | Y Mean: 63.4, Y Variance: 2.8
The Y-X difference column has not been computed. You need to fill this out and compute the corresponding mean and variance (for Y-X) for question
3.
Test whether the population mean of Y is no greater than 1/2 (0.5) unit higher than the population mean for X as the null hypothesis (Ho) vs the
population mean of Y is more than 1/2 unit greater than the population mean for X as the alternative hypothesis (H1).
What is the small sample t statistic for the test of Ho? Round to two decimal places (e.g., 1.23)
Assume the measurements are independent (not a paired test), the variances are not equal and the degrees of freedom for the small sample test can be
approximated by 5 + 5 -2 = 8.
Transcribed Image Text:Questions 1, 2, 3, and 4 use the X and Y data below. You can think of this data as representing the heights of 5 individuals (labelled A,B,C,D,E) at ages 11 (X column) and 12 (Y column). Paired Y-X Obs X A B с D E 60 61 62 63 64 Y 62 62 63 64 66 The means and variances for X and Y are shown below. (You can verify to practice calculation steps.) X Mean: 62, X Variance: 2.5 | Y Mean: 63.4, Y Variance: 2.8 The Y-X difference column has not been computed. You need to fill this out and compute the corresponding mean and variance (for Y-X) for question 3. Test whether the population mean of Y is no greater than 1/2 (0.5) unit higher than the population mean for X as the null hypothesis (Ho) vs the population mean of Y is more than 1/2 unit greater than the population mean for X as the alternative hypothesis (H1). What is the small sample t statistic for the test of Ho? Round to two decimal places (e.g., 1.23) Assume the measurements are independent (not a paired test), the variances are not equal and the degrees of freedom for the small sample test can be approximated by 5 + 5 -2 = 8.
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