Free Two sample intervals for proportions Practice Problems • Learn To Be

Peter owns two bakeries. One of them is in a large city and the other is in a small town. He wants to see if more people prefer his triple chocolate cake over his chocolate cream pie in the town than in the city.

Peter has compiled a list of

3{,}000

regular customers that visit his city bakery and

1{,}000

that visit his town bakery. He randomly selects

200

customers from the city location and

50

from the town location and discovers that

120

of the city customers sampled and

45

of the town customers sampled prefer the triple chocolate cake over the chocolate cream pie. Peter then asks his statistician friend for help constructing a

95\%

confidence interval for the difference between the proportion of people who prefer the triple chocolate cake over the chocolate cream pie at the town bakery and at the city bakery.

The friend tells him:

Choose 1 answer:

A
His confidence interval is $\left(0.19,0.41\right)$ .
B
His confidence interval is $\left(0.21,0.39\right)$ .
C
He cannot accurately construct the confidence interval because the data did not come from two independent random samples.
D
He cannot accurately construct the confidence interval because he may not reasonably approximate the standard error of the difference in sample means using the formula $SE_{\hat{p}_1-\hat{p}_2}=\sqrt{\dfrac{\hat{p}_1\left(1-\hat{p}_1\right)}{n_1}+\dfrac{\hat{p}_2\left(1-\hat{p}_2\right)}{n_2}}$ .
E
He cannot accurately construct the confidence interval because he may not reasonably assume that the sampling distribution of the difference in sample proportions is approximately normal.

Two sample intervals for proportions

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