Question

According to the internet, the average (mean) height of adult men in the U.S. is 69.3 inches tall (about 5 foot, 9 inches tall). That seems wrong to me, and so I decided to test whether or not that is true by measuring the heights of a random sample of 63 adult men. I find that my sample of 63 women has a mean height of 71.2 inches and a standard deviation of 1.2 inches.

Answer the following questions in the space provided below:

1. State the null and alternative hypotheses. (Type mu instead of using the symbol.)
2. Find the standard error of the distribution of sample statistics (null distribution). You will need to use one of the formulas for standard error from your formula sheet. Write down the formula you used and round the answer to one decimal place.
3. Find the t-score for our observed statistic for this example.
4. Formulate a conclusion based on your t-score.

Answer 1

Here hypothesis are

H0 : = 69.3 inches

Ha : 69.3 inches

sample size = n = 63

sample mean = = 71.2 inches

sample standard deviation = s= 1.2 inches

standard error of sample mean = s/sqrt(n) = 1.2/sqrt(63) = 0.1512 inches

Test statistic

t = (71.2 - 69.3)/0.1512 = 12.57

Degree of freedom = dF = n -1 = 63 -1 = 62

Here critical value of t statistic = TINV(0.05, 62) = 1.999

so here t > t statistic so we would reject the null hypothesis and conclude that population mean of adult men is not equal to 69.3 inches.