Question

The National Center for Health Statistics (NCHS) provides statistical information that guides actions and policies to improve the health of the American people.Recent data from NCHS give the average height of females in the United

States to be 63.7 inches, with a standard deviation of 2.75 inches. A random sample of 50 females from the health profession yielded the following height data:

65.0 66.0 64.0 67.0 59.0 69.0 66.0 69.0 64.0 61.5

63.0 62.0 63.0 64.0 72.0 66.0 65.0 64.0 67.0 68.0

70.0 63.0 63.0 68.0 58.0 60.0 63.5 66.0 64.0 62.0

64.5 69.0 63.5 69.0 62.0 58.0 66.0 68.0 59.0 56.0

64.0 66.0 65.0 69.0 67.0 66.5 67.5 62.0 70.0 62.0

(e) Does the mean m _ 63.7 fall in the interval? Explain what this means.

(f) Describe the relationship between the two lines drawn on your graph for part c of question 3 and the two lines drawn for part d of this exercise.

(g) On the basis of the results obtained earlier, does it appear that the females in this study, on average, are the same height as all females in the United States as reported by the NCHS? Explain

Answer 1

Here

sample mean

sample standard deviation

and sample size n = 50

e) a 95% confidence interval for population mean of height of females in the United States

g) Let denotes the population mean of height of females in the United States.

To test against

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 5% level of significance if

Here

The value of the test statistic

and the critical value

Since , we reject H₀ at 5% level of significance and we can conclude that the mean is significantly different from the average height of all females in the United States as reported by the NCHS.