Question

 

Find all variables( SE, z or t, P-value, p hat, etc)

1) Last semester, a student at Waseda University polled a random sample of 400 ex-maiko in Kyoto and discovered 0.18 of the women went on to become geiko. Furthermore, he discovered that these women who became geiko had an average height of 65 inches (165 cm) and a standard deviation of 6 cm.

a) Find an appropriate 80% confidence interval. (Round data to five decimal places)

b) A student at Kyoto University thought the baseline was 159 cm. Perform a hypothesis test to check your results from above. What is the conclusion of your hypothesis test?

Answer 1

a)

sample mean, xbar = 165
sample standard deviation, s = 6
sample size, n = 400
degrees of freedom, df = n - 1 = 399

Given CI level is 80%, hence α = 1 - 0.8 = 0.2
α/2 = 0.2/2 = 0.1, tc = t(α/2, df) = 1.284

ME = tc * s/sqrt(n)
ME = 1.284 * 6/sqrt(400)
ME = 0.385

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (165 - 1.284 * 6/sqrt(400) , 165 + 1.284 * 6/sqrt(400))
CI = (164.6148 , 165.3852)

b)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 159
Alternative Hypothesis, Ha: μ ≠ 159

Rejection Region
This is two tailed test, for α = 0.01 and df = 399
Critical value of t are -2.588 and 2.588.
Hence reject H0 if t < -2.588 or t > 2.588

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (165 - 159)/(6/sqrt(400))
t = 20

P-value Approach
P-value = 0
As P-value < 0.2, reject the null hypothesis.