Question

Find the standard deviation, upper and lower values, and include graphical representations of the rejection region, p-value and the confidence interval

According to data, 72.4% of the population in Kahului, Maui drive alone for their commute to work. You believe this is too high and will perform a study at a 5% level of significance. A group of 30 people were sampled in Kahului, Maui where 21 people stated that they drive alone for their commute to work

Answer 1

H0: p = 0.724
Ha: p < 0.724

pcap = 21/30 = 0.7

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.7 - 0.724)/sqrt(0.724*(1-0.724)/30)
z = -0.29

standard deviation = sqrt(0.724*(1-0.724)/30) = 0.0816

p-value = 0.3859

As p-value > 0.05, we fail to reject H0
There are not significant evidence to conclude that less than 0.724 drive alone for their commute to work.

Confidence Interval:
sample proportion, pcap = 0.7
sample size, n = 30
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.7 * (1 - 0.7)/30) = 0.0837

For 95% Confidence level, the z-value = 1.96
CI = (xbar - z*SE, xbar + z*SE)
CI = (0.7 - 1.96 * 0.0837 , 0.7 + 1.96 * 0.0837)
CI = (0.5359 , 0.8641)