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Chapter 7: Q. 39 (page 441)

Students on diets A sample survey interviews an SRS of 267college women. Suppose (as is roughly true) that 70% of college women have been on a diet within the past 12 months. What is the probability that 75% or more of the women in the sample have been on a diet? Follow the four-step process.

Short Answer

Expert verified

The probability that 75%or more of the women in the sample have been on a diet is0.0375.

Step by step solution

01

Given Information 

Number of SRS=267

The proportion of women on a diet within the past 12months =70%

02

Explanation 

We have,

p=70%=0.70

p^=75%=0.75

n=267

p^ is equal to the percentage of the population p in the sampling distribution:

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Most popular questions from this chapter

Doing homework Refer to Exercise 9.

(a) Make a graph of the population distribution given that there are 3000 students in the school. (Hint: What type of variable is being measured?)

(b) Sketch a possible graph of the distribution of sample data for the SRS of size 100 taken by the AP Statistics students.

Run a mile During World War II, able-bodied male undergraduates at the University of Illinois participated in required physical training. Each student ran a timed mile. Their times followed the Normal distribution with mean 7.11minutes and standard deviation 0.74minute. An SRS of 100of these students has mean time x炉=7.15minutes. A second SRS of size100has mean x炉=6.97minutes. After many SRSs, the values of the sample mean x follow the Normal distribution with mean 7.11 minutes and standard deviation0.074minute.

(a) What is the population? Describe the population distribution. (b) Describe the sampling distribution of x. How is it different from the population distribution?

Decreasing the sample size from 750to 375would multiply the standard deviation by

(a) 2.

(b) 2.

(c) 1/2.

(d) 1/2.

(e) none of these.

Are the events 鈥渋n the labor force鈥� and 鈥渃ollege graduate鈥� independent? Justify your answer .

Which of the following statements about the sampling distribution of the sample mean is incorrect? (a) The standard deviation of the sampling distribution will decrease as the sample size increases.

(b) The standard deviation of the sampling distribution is a measure of the variability of the sample mean among repeated samples.

(c) The sample mean is an unbiased estimator of the true population mean.

(d) The sampling distribution shows how the sample mean will vary in repeated samples.

(e) The sampling distribution shows how the sample was distributed around the sample mean
See all solutions

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