Question

3.   The heights of women in the fictional country of Rohkia follow a Normal distribution. You’d like to perform a hypothesis test to see if the average height of Rohkian women is significantly more than 61 inches.
   You select 8 women at random and measure their heights (in inches), which are recorded in the table below.
61
61
62
64
67
63
64
62

a.   Find the mean and standard deviation of the heights in the sample. Use the correct symbols for this sample data.
b.   Write hypotheses to test whether the population height is over 61 inches.
c.   Perform the calculations for the test. Please report the value of test statistic (t) and the p-value.
d.   Can we conclude the mean height of Rohkian women is significantly greater than 61 inches? Explain why or why not. (Use α = 0.05)

Answer 1

a)
mean=   63.00    [Excel function used -> AVERAGE]
sd=   2.00    [Excel function used -> STDEV]

b)
ho: the average height of Rohkian women is equal to 61 inches.
h1: the average height of Rohkian women is more than 61 inches.

c)
test statistic, t = (mean-u)/(sd/sqrt(n))
= (63-17)/(2/sqrt(8))
= 65.0538

p-value
(1-P(T<t)
1-P(T<65.0538)
t.dist.rt(65.0538,8-1)
2.66442E-11

d)
With t=65, p<5%, i reject Ho at 5% level of significacne and conclude that the average height of Rohkian women is more than 61 inches.