Question

Comfort Food Magazine states that the percentage of people who like to eat hot dogs is 55%. A random selection of 275 people are asked if they like eating hot dogs and 55% said they do. At the α = 0.09 level, is there sufficent evidence to conclude that the percentage of people that like to eat hot dogs is higher than 55%?

Answer 1

Given that the Comfort, Food Magazine states that the percentage of people who like to eat hot dogs is p = 55%. A random selection of n = 275 people is asked if they like eating hot dogs and = 55% said they do. At the α = 0.09 level the hypotheses are:

Ho : P =0.55

Ha : P>0.55

Based on the hypothesis it will be a right-tailed test.

Requirements:

Before conducting the hypothesis test we need to check certain requirements for the proportions as:

1) n*P(1-P) >=10, so, 275*0.55(1-0.55) = 60.06- Satisfied.

2) The sample is random- True, Satisfied.

Snince both requirements are satisfied hence we can further proceed assuming the distribution is normal and Z-distribution is applicable for hypothesis testing.

Rejection region:

Reject the Ho if P-value is less than the given level of significance which is 0.05

Test Statistic:

P-value:

The P-value for the Z test is calculated using the excel formula for normal distribution which is =1-NORM.S.DIST(0, TRUE), thus the P-value is computed as 0.500.

Conclusion:

Since the P-value is greater than 0.05 hence we failed to reject the null hypothesis, hence we conclude that there is insufficient evidence to support the claim that the percentage of people that like to eat hot dogs is higher than 55%.

Note: I urge you to check your data first.