Question

A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than

14.514.5

seconds. A random sample of

2222

sedans has a mean minimum time to travel a quarter mile of

15.415.4

seconds and a standard deviation of

2.112.11

seconds. At

alphaαequals=0.050.05

is there enough evidence to support the consumer​ group's claim? Complete parts​ (a) through​ (d) below. Assume the population is normally distributed.

Answer 1

The null and alternativ ehypothesis is ,

The test is one-tailed test.

Since , the population standard deviation is not known.

Therefore , use t-test.

Now , df=degrees of freedom=n-1=22-1=21

The critical value is ,

; From t-table

The test statistic is ,

Decision : Here , the value of the test statistic lies in the rejection region.

Therefore , reject Ho.

Conclusion : Hence , there is enough evidence to support the consumer group's claim.