Question

Use the six-step hypothesis testing where appropriate:

1. You have been told that the mean price of two movie tickets including online service charges, a large popcorn, and two medium soft drinks is $38. Based on a sample of 10 theater chains and assuming a normal distribution, the sample mean was found to be $36.53 and the standard deviation was $3.38. At the 0.05 level of significance, is there enough evidence to indicate that the average price is now less than $38?

a. What is the appropriate null and alternative hypothesis for problem 1? Use both words and notations

b.What level of significance and sample size is used in this problem?

c.What type of problem is this? What formula will you use? Why?

d. What is the correct critical value for the problem? How did you find it?

e.What is the correct value for the test statistic? Provide the formula used and show work

f. Should you accept or reject the null hypothesis? How much confidence do you have in your decision? Restate the null of alternative hypothesis. What policy decision would you make?

Answer 1

A)

Null hyppthesis Ho : u = $38

Alternate hypothesis Ha : u < $38

Null hypothesis is that average price is $38

Alternate hyppthesis is that average price is less than $38

B)

Significance used = 0.05

Sample size = n= 10

C)

As the population standard deviation is unknown, we will use one sample t-test

We will use test statistics formula

T = (sample mean - claimed mean)/(s.d/√n)

D)

First we need to estimate the degrees of freedom

Degrees of freedom is given by n-1

10-1, 9

For df 9 and significance level of 0.05

From t table required critical value is = -1.833

E)

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

Sample mean = 36.53

S.d = 3.38

N = 10

t = −1.375310106641

F)

Rejection region is if obtained test statistics is less than the critical value

As -1.375 (obtained test statistics) is not less than the -1.833 (critical value)

We fail to reject the null hypothesis.

There is not sufficient evidence to support the claim that the average price is now less than $38