Question

Many Alpine ski centers base their calculations of revenues and profits on the belief that the average skier ski’s four times a year with a population standard deviation of 2. To investigate this belief a random sample of 63 skiers was drawn and each participant was asked to report the number of times they skied last year. This yielded a mean of 4.84. Can we infer at the 10% significance level that the assumption of ski centers is wrong?

Answer 1

here we want to test the

null hypothesis H0: =4 and alternate hypothesis Ha: ( this is two tailed test)

since population standard deviation is known/given so we use z-test and z=(-)/(/)=(4.84-4)/(2/sqrt(63))=3.33

the two tailed critical z(0.1/2)=1.645 is less than calculated/observed z=3.334 so we reject H0 and conclude that average skier ski’s four times a year is not true and assumption of ski centers is wrong.