Question

Some candy bars include a voucher for a free movie. The candy company claims that a voucher can be found in ten percent of candy bars. However, based on their experiences buying these candy bars, a group of students believes that the proportion of candy bars with vouchers is lessthan ten percent. To test the company’s claim, the students purchased 60 candy bars and founda total of 3 vouchers. Use a 0.05 significance level to test the claim that the proportion of candy bars with vouchers is less than ten percent.

a. State the appropriate null and alternative hypotheses. b. Compute the test statistic.
c. Compute the P-value for this test.
d. Show decision criteria and state a conclusion.

Answer 1

a)

H0: p = 0.10

Ha: p < 0.10 (Left tailed)

b)

Sample proportion = 3 / 60 = 0.05

Test statistics

Z = - p / sqrt( p( 1 - p) / n)

= 0.05 - 0.10 / sqrt( 0.10 * 0.90 / 60)

= -1.291

This is value of test statistics

c)

p-value is calculated as

p-value = P( Z < -1.291)

= 1 - P( Z < 1.291)

= 1 - 0.9016

= 0.0984

d)

Since p-value > 0.05 significance level, we do not have sufficient evidence to reject H0.

We conclude at 0.05 level that we fail to support the claim that the proportion of candy bars with

vouchers is less than ten percent.