Question

In: Statistics and Probability

Indicate the test you would use and the reason (e.g. One sample test for the variance...

Indicate the test you would use and the reason (e.g. One sample test for the variance of a normal distribution)

  1. One sample z test for the mean of a normal distribution with known variance (Test 1*)
  2. One Sample T Test for the Mean of a Normal Distribution with unknown Variance (Test 2)
  3. The paired t-test (Test 3)

  1. A researcher wants to test the effect of using a lumbar support pillow on angular position of the pelvis in relaxed sitting. The researcher hypothesizes that pelvic tilt will change with use of a support pillow (a non-directional hypothesis). The researcher tests eight subjects, each one sitting relaxed in a straight-back chair with and without the pillow (in random order). The angle of the pelvic tilt is measured using a flexible ruler, with measurements transformed to degrees.

Test______________ Why?____________________

  1. We have a one-tailed test, a = .05, σ known, n = 20

Test______________ Why?____________________

  1. We have a two-tailed test, a = .05, σ unknown, n = 35

Test______________ Why?__________________

  1. Suppose the distribution of systolic blood pressure in the general population is normally distributed with a mean of 130 mm and standard deviation of 20 mm. We find in a special subgroup of 85 persons with glaucoma that the mean systolic blood pressure is 135 mm with a standard deviation of 22 mm. assuming that the standard deviation of the glaucoma group is the same as the general population, test for an association between glaucoma and high blood pressure.

Test______________ Why?____________________

Solutions

Expert Solution

## a) A researcher wants to test the effect of using a lumbar support pillow on angular position of the pelvis in relaxed sitting. The researcher hypothesizes that pelvic tilt will change with use of a support pillow (a non-directional hypothesis). The researcher tests eight subjects, each one sitting relaxed in a straight-back chair with and without the pillow (in random order). The angle of the pelvic tilt is measured using a flexible ruler, with measurements transformed to degrees.

Answer : it is paired test because we tests with and without ( ie before and after ) type and check the angle of pelvic tilt individual person . (test 3 is used )

## b) We have a one-tailed test, a = .05, σ known, n = 20

Answer : here we can use small sample z  test because we σ known that why z test is prefer (small z test)

## c) We have a two-tailed test, a = .05, σ unknown, n = 35

Answer : here we can use t test because σ unknown,

## d) Suppose the distribution of systolic blood pressure in the general population is normally distributed with a mean of 130 mm and standard deviation of 20 mm. We find in a special subgroup of 85 persons with glaucoma that the mean systolic blood pressure is 135 mm with a standard deviation of 22 mm. assuming that the standard deviation of the glaucoma group is the same as the general population, test for an association between glaucoma and high blood pressure.

Answer : here we can use z test because we know the population variance that is known standard deviation .


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