Question Type 5: Performing a hypothesis test on single proportion using the binomial distribution Exercises

A company asserts that 60% of its visitors subscribe on their first visit. In a sample of 150 visitors, 80 subscribe. At the 10% significance level, test whether the true subscription rate exceeds 60%.

A website claims that 55% of its users make a purchase on their first visit. A researcher surveys 190 users and finds 45 purchases. At the 5% significance level, test whether the true purchase rate is less than 55%.

A poll indicates 70% support for a policy. In a sample of 200 people, 120 support it. At the 5% significance level, test whether the support differs from 70%.

A hospital averages 5 infection cases per month. After a new protocol, 1 month yields 2 cases. At 5% significance, test if the infection rate has decreased (Poisson test).

A shampoo factory produces on average 4 faulty bottles per 200. After installing a new machine, 400 bottles are inspected and 2 are faulty. At the 5% level, test whether the fault rate has decreased using the Poisson model.

It is claimed that 50% of users click an ad within 10 seconds. A sample of 220 users yields 95 clicks. At 5% significance, test if the click rate is less than claimed.

A process has 3 defects per 100 items on average. After an update, 1,000 items yield 25 defects. At 5% level, test for a decrease using normal approximation of Poisson.

A factory averages 4 faulty items per 200 produced. After changes, 1,400 items are checked and 14 faults are found. At 5% significance, test for improvement using a normal approximation to Poisson.

Traffic studies show 2 accidents per day on average. After a safety campaign over 14 days there are 10 accidents. At 5% level, test for improvement using Poisson.

A process has historically 3 defects per 100 items. After improvement, 300 items are checked and 6 defects are found. At the 1% significance level, test for a reduction using a Poisson model.

A clinic records on average 5 infections per month. Over 12 months after an intervention, 50 infections occur. At 5% significance, test for a reduction using normal approximation to Poisson.

A city averages 2 road accidents per day. Over the past year (365 days), 680 accidents occurred. At 5% significance, test whether the daily accident rate has decreased using the normal approximation to Poisson.