Perform each hypothesis test. For each exercise, complete the following steps: S
ID: 3312811 • Letter: P
Question
Perform each hypothesis test. For each exercise, complete the following steps:
State the null and alternative hypothesis.
Determine which distribution to use for the test statistic, and state the level of significance.
Calculate the test statistic.
Draw a conclusion comparing the p-value to the level of significance.
Sleep apnea is a condition in which the sufferers stop breathing momentarily while they are asleep. This condition results in lack of sleep and extreme fatigue during waking hours. A current estimate is that 18 million out of the 312.7 million Americans suffer from sleep apnea, or approximately 5.8%. A safety commission is concerned about the percentage of commercial truck drivers who suffer from sleep apnea. They do not have any reason to believe that it would be higher or lower than the population’s percentage. To test the claim that the percentage of commercial truck drivers who suffer from sleep apnea is not 5.8%, a simple random sample of 350 commercial truck drivers is examined by a medical expert, who concludes that 30 suffer from sleep apnea. Does this evidence support the claim that the percentage of commercial truck drivers show suffer from sleep apnea is not 5.8%? Use a 0.01 level of significance.
Source: American Sleep Apnea Association. “Sleep Apnea” 2011
Source: US Census Bureau. “American FactFinder
TransAir, an international airline company, has a new jumbo jet that it believes will decrease the mean transatlantic flight time from Newark to London Heathrow. In order to be faster than its competitors, the mean must be less than 6 h 50 min. Because of costs, the agency monitoring the flight times only requires that eight trials be run. The results are given in the table below. If the FAA requires that the agency be 90% confident of its findings, what should the agency report? Assume that the population distribution is approximately normal.
Flight Times from Newark to London
Flight
Flying Time
Flight 1
6 hr 32 min
Flight 2
6 hr 28 min
Flight 3
6 hr 51 min
Flight 4
6 hr 2 min
Flight 5
6 hr 51 min
Flight 6
7 hr 2 min
Flight 7
6 hr 36 min
Flight 8
6 hr 42 min
Flight Times from Newark to London
Flight
Flying Time
Flight 1
6 hr 32 min
Flight 2
6 hr 28 min
Flight 3
6 hr 51 min
Flight 4
6 hr 2 min
Flight 5
6 hr 51 min
Flight 6
7 hr 2 min
Flight 7
6 hr 36 min
Flight 8
6 hr 42 min
Explanation / Answer
Below are the null and alternate hypothesis
H0: p = 0.058
H1: p not equals to 0.058
z-distribution can be used here
pcap = 30/350 = 0.0857
SE = sqrt(0.058*0.942/350) = 0.0125
Test statistics, z = (0.0857 - 0.058)/0.0125 = 2.216
p-value = 0.0135*2 = 0.0267
As p-value is greater than the significance level of 0.01, we fail to reject the null hypothesis.
Hence there are not significant evidence to conclude that the percentage of commercial truck drivers show suffer from sleep apnea is not 5.8%
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