Question

A blind taste test is conducted to determine which of two colas, Brand A or Brand B, individuals prefer. Individuals are randomly asked to drink one of the two types of cola first, followed by the other cola, and then asked to disclose the drink they prefer. Results of the taste test indicate that 56 of 100 individuals prefer Brand A. Complete parts a through c.

A) Conduct a hypothesis test H0: p=p0 verus H1: p not equal 0.45, 0.46, 0.47,... 0.65, 0.66, 0.67 at the a=0.05 level of significance. for which values of p- do you not reject the null hypothesis? what do each of the values of p0 represent?

B) Construct a? 95% confidence interval for the proportion of individuals who prefer Brand A. The lower bound is _. The upper bound is _.

C) Suppose you changed the level of significance in conducting the hypothesis test to a= 0.01. What would happen to the range of values for p0 for which the null hypothesis is not? rejected? Why does this make? sense? Choose the correct answer below.

A.The range of values would decrease because the corresponding confidence interval would increase in size.

B. The range of values would increase because the corresponding confidence interval would increase in size.

C. The range of values would increase because the corresponding confidence interval would decrease in size.

D. The range of values would decrease because the corresponding confidence interval would decrease in size

Answer 1

(a)

The sample proportion is:

Following is the output of z test of proportion:

The p-value is increases as the value of p0 increases. Since p-value for p0 = 0.47 is greater than 0.05 so we will not reject the null hypothesis for p0 =0.47.

Now intuitively, let us check out for three upper ended values 0.65, 0.66, 0.67. Following is the output:

Since p-values for p0 = 0.66 (so it will less for 0.67 also) is less than 0.05 so we will reject the null hypothesis for these values.

That is range of values for which we will not reject the null hypothesis is 0.47 to 0.65 (inclusive).

Answer: 0.47 to 0.65 (inclusive)

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(b)

Following is the output of confidence interval:

The 95% confidence interval is (0.463, 0.657).

The lower bound is: 0.463

The upper bound is: 0.657

(c)

B. The range of values would increase because the corresponding confidence interval would increase in size.