1. What type of car is more popular among college students, American or foreign? One hundred fifty-nine college students were randomly sampled and each was asked which type of car he or she prefers. A computer package was used to generate the printout below for the proportion of college students who prefer American automobiles.

SAMPLE PROPORTION = .0.388630
SAMPLE SIZE = 159

UPPER LIMIT = .464240
LOWER LIMIT = .331153

What point estimate for the proportion of students prefer foreign automobiles?
A) .0.388630
B) .464240
C) .331153
D) .0.61137

I am having trouble answering this problem? I don't know where to begin.

2. A marketing research company is estimating which of two soft drinks, Mountain Dew or Coke, college students prefer. A random sample of 88 college students produced the following 95% confidence interval for the proportion of college students who prefer Mountain Dew: (0.071, 0.093)

Is the sample size large enough for the interval to be valid?
A) No, the sample size is too small.
B) Yes, the sample was randomly selected from an approximately normal population.
C) No, since mathml equation the sample size is not large enough.
D) Yes, since we know that there are more than 880 college students.

I would say D is the answer because of the population size. Please check my answer. Thx!

I have to disagree with the choice of A. That is based on preference for American cars not Foreign cars.

1. In the given scenario, a random sample of 159 college students was taken to determine their preference for American automobiles. The sample proportion was calculated as 0.388630, with an upper limit of 0.464240 and a lower limit of 0.331153.

To find the point estimate for the proportion of students who prefer foreign automobiles, you can subtract the sample proportion from 1.

Point estimate for the proportion of students who prefer foreign automobiles = 1 - 0.388630 = 0.61137

Therefore, the correct answer is D) 0.61137.

2. In this scenario, a random sample of 88 college students was taken to estimate which soft drink, Mountain Dew or Coke, college students prefer. The calculated 95% confidence interval for the proportion of college students who prefer Mountain Dew is (0.071, 0.093).

To determine if the sample size is large enough for the interval to be valid, you need to consider the requirements for a valid confidence interval. For proportions, a general rule is that both np and n(1-p) should be greater than 10, where n is the sample size and p is the proportion. In this case, the sample size is 88, and the midpoint of the confidence interval is (0.071+0.093)/2 = 0.082.

np = 88 * 0.082 = 7.216, and n(1-p) = 88 * (1 - 0.082) = 80.544

Both np and n(1-p) are greater than 10, so the sample size is indeed large enough for the interval to be valid.

Therefore, the correct answer is B) Yes, the sample was randomly selected from an approximately normal population.

1. To determine the point estimate for the proportion of students who prefer foreign automobiles, we need to subtract the point estimate for the proportion of students who prefer American automobiles (0.388630) from 1. Since the sample size is 159, we can calculate the point estimate for the proportion of students who prefer foreign automobiles as follows:

Point Estimate for Foreign Automobiles = 1 - Point Estimate for American Automobiles
= 1 - 0.388630
= 0.611370

Therefore, the correct answer is D) 0.61137.

2. The validity of a confidence interval depends on the sample size and the underlying population distribution. In this case, we are given that the sample size is 88 and the confidence interval is (0.071, 0.093). To determine if the sample size is large enough for the interval to be valid, we need to assess if the sample was randomly selected from an approximately normal population.

It was not mentioned whether the population follows an approximately normal distribution. However, the sample size of 88 is generally considered large enough for the central limit theorem to apply, which allows us to assume that the sampling distribution of sample proportions is approximately normal. Therefore, the correct answer is B) Yes, the sample was randomly selected from an approximately normal population.

Note: The answer choice D) Yes, since we know that there are more than 880 college students is irrelevant in this context, as it does not directly address the validity of the confidence interval.

1. The best point estimate for p is the sample proportion. Answer: A

2. I agree with your choice.