In a simple random sample of 36 colored candies it is found

In a simple random sample of 36 colored candies, it is found that none of them are blue. Use a 0.01 significance level to test the claim of the candy company that the proportion of candies that are blue is equal to 0.10. Can a hypothesis test for a claim about the population proportion be used? If so, test the claim. If not, explain why not.

1) Can a hypothesis test for a claim about the population proportions be used.

a) Both the normal distribution and the binomial distribution can be used for a hypothesis test of these data.

b) Neither the normal distribution nor the binomial distribution can be used for a hypothesis test on these data.

c) The normal distribution can be used for a hypothesis test on these data, but the normal distribution cannot be used for a hypothesis test on these data.

d) The binomal distribution can be used for a hypothesis test on these data, but the normal distribution cannot be used for a hypothesis test on these data.

2) Identify the null hypothesis and alternative hypothesis

a) H0: p = 0.1          H1: p < 0.1

b) H0: p = 0.1.        H1: p not= 0.1

c) H0: p = 0.1.         H1: p > 0.1

3) Identify the test statistic. Select the correct choice and, if necessary, fill in the answer box to complete your choise.

a) The test statistic is ___

b) There is no test statistic because the binomial distribution must be used for this test

c) A hypothesis test cannot be used for these data

4) Select the correct choice and, if necessary, fill in the answer box to complete your choice,

a) The P-value is ___

b) A hypothesis test cannot be used for these data.

5) Draw a conclusion.

a) Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the proportion of candies that are blue is equal to 0.10

b) Fail to reject the null hypothesis. There is insufficient evidence to warrant rejection of the claim that the proportion of candies that are blue is equal to 0.10

c) Reject the null hypothesis. There is insufficient evidence to support the claim that the proportion of candies that are blue is equal to 0.10

d) Reject the null hypothesis. There is sufficient evidence to support the claim that the proportion of candies that are blue is equal to 0.10

e) A hypothesis test cannot be used for these data.

Solution

1) Can a hypothesis test for a claim about the population proportions be used.

d) The binomal distribution can be used for a hypothesis test on these data, but the normal distribution cannot be used for a hypothesis test on these data because normal distribution can be used only when np and nq both are greater than 5. Here n=36 and p=0.1. Therefore np=36(0.1)=3.6 which is less than 5.

2) Identify the null hypothesis and alternative hypothesis

b) H0: p = 0.1.        H1: p 0.1

3) Identify the test statistic. Select the correct choice and, if necessary, fill in the answer box to complete your choice.

Since we are using binomial distribution, the test statistic would be x value.

a) The test statistic is x=0.

4) Select the correct choice and, if necessary, fill in the answer box to complete your choice.

Here n=36 and p=0.1.

p-value = Binompdf(36,0.1,0) = 0.0225

a) The P-value is 0.0225.

5) Draw a conclusion.

Since p-value is greater than 0.01 (given level of significance), fail to reject the null hypothesis.

b) Fail to reject the null hypothesis. There is insufficient evidence to warrant rejection of the claim that the proportion of candies that are blue is equal to 0.10.