Questions 1 and 2 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). Obs X Y Paired Y-X A 60 62 B 61 62 C 62 63 D 63 64 E 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 2 1) 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. 2) Now treat X and Y as non-independent measurements, where and the values in each row are for the same individual (at age 11 and then age 12). Compute the small sample paired-difference t statistic for the same null and alternative hypotheses. (Round your answer to 2 decimal places)
Questions 1 and 2 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).
| Obs | X | Y | Paired Y-X |
|---|---|---|---|
| A | 60 | 62 | |
| B | 61 | 62 | |
| C | 62 | 63 | |
| D | 63 | 64 | |
| E | 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 2
1) 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.
2) Now treat X and Y as non-independent measurements, where and the values in each row are for the same individual (at age 11 and then age 12). Compute the small sample paired-difference t statistic for the same null and alternative hypotheses. (Round your answer to 2 decimal places)
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