Question

Many ski resorts base their projection of revenues and profits on the assumption that the average skier skis 4 times per year. A random sample of 63 skiers is drawn and each skier is asked to indicate the number of times he or she skied the previous year. The dataset Qn9.1 contains the responses for each skier. Assume that the population standard deviation is 2. [ Hint: Use an appropriate Excel template from chapter 9 or formulas] a. Formulate the null and alternative hypothesis that can be used to test the assumption made by ski resorts. b. Compute the value of the test statistic c. What is the p-value? d. At α = .05, what is the critical value? e. At α = .05, what is your conclusion? Ski Days 4 6 5 5 6 2 6 5 1 9 7 5 2 6 5 7 1 6 6 5 6 3 5 5 4 4 5 6 0 4 1 5 6 4 7 6 3 5 6 8 6 6 1 5 4 6 8 1 5 5 5 3 6 4 7 2 10 3 6 6 2 4 8

Answer 1

Ans:

a)

b)

n=63

Sample mean=4.841

Test statistic:

z=(4.841-4)/(2/SQRT(63))

z=3.34

c)

p-value(2 tailed)=2*P(z>3.34)=0.0008

d)critical z value=+/-1.96

e)

As,p-value<0.04,we reject the null hypothesis.

There is sufficient evidence to reject the claim that the average skier skis 4 times per year.