STATS – We are studying the first-year performance of small start-up businesses

| August 30, 2017

Question
1. We are studying the first-year performance of small start-up businesses. We wish to determine whether the proprietor’s equity percentage is different for those that fail than for those that succeed. We randomly sample records for start-up businesses and obtain the following sample results:

Failures Successes

n: 15 17

sample mean %: 5.73 7.88

s: 3.33 2.55

Perform an appropriate hypothesis test to determine whether the proprietor’s

equity percentage for the failures is different than that for the successes.

2. On the Road Again, Inc. maintains a large fleet of rental cars. They want their fleet to have an average of at least 25 mpg. They will determine this based on an appropriate 1-sided hypothesis test with?= 0.10. They sample 36 cars at random and find a sample mean of 25.35 mpg with a sample standard deviation of 3.24 mpg. Compute the appropriate test statistic and give the conclusion of the test.

3. Consider the following hypothesis test:
H0: ?= 17
Ha: ? ? 17
? = 0.05
It is decided to conduct the test by computing a 2-sided 95% confidence interval and basing the
test conclusion on it. Based on a properly taken sample, the valid 2-sided 95% confidence interval
is computed to be (15.515, 17.775). Based on this, what is the conclusion of the hypothesis test?

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