Question

The mean time that all voters spent at polling booths in Small City is 60 seconds. A student suspects that the mean time that voters spent at a high school polling booth is less than 60 seconds. She selected a random sample of 30 voters and recorded the times they spent at the polling booth. The sample mean is 54 seconds and the sample standard deviation is 24 seconds. At the 0.05significance level, do the data show sufficient evidence that the mean time that voters spent at the high school polling booth is less than 60 seconds? (a) H0: Ha: (b) The hypothesis test is _____ tailed. (c) Test statistic t = (d) df = (e) p-value = (f) Decision: ___ (Reject, Fail to reject) H0. (g) Interpretation:

Answer 1

a)

H0: = 60

Ha: < 60

b)

This hypothesis test is left tailed.

c)

Test statistics

t = - / S / sqrt(n)

= 54 - 60 / 24 / sqrt(30)

= -1.37

d)

df = n - 1= 30 - 1 = 29

e)

From T table,

With test statistics -1.37 and df 29,

p-value = 0.0906

f)

Since p-value > 0.05 significance level, do not reject the null hypothesis.

g)

We conclude at 0.05 level that we do not have sufficient evidence to support the claim.