Question

According to the website www.collegedrinkingprevention.gov, “About 25 percent of college students report academic consequences of their drinking including missing class, falling behind, doing poorly on exams or papers, and receiving lower grades overall.” A statistics student is curious about drinking habits of students at his college. He wants to estimate the mean number of alcoholic drinks consumed each week by students at his college. He plans to use a 99% confidence interval. He surveys a random sample of 55 students. The sample mean is 3.69 alcoholic drinks per week. The sample standard deviation is 3.56 drinks.

Construct the 99% confidence interval to estimate the average number of alcoholic drinks consumed each week by students at this college.

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Your answer should be rounded to 2 decimal places.

Question 5

Estimating Mean SAT Math Score

The SAT is the most widely used college admission exam. (Most community colleges do not require students to take this exam.) The mean SAT math score varies by state and by year, so the value of µ depends on the state and the year. But let’s assume that the shape and spread of the distribution of individual SAT math scores in each state is the same each year. More specifically, assume that individual SAT math scores consistently have a normal distribution with a standard deviation of 100. An educational researcher wants to estimate the mean SAT math score (μ) for his state this year. The researcher chooses a random sample of 695 exams in his state. The sample mean for the test is 487.

Find the 90% confidence interval to estimate the mean SAT math score in this state for this year.

(Note: The critical z-value to use, zc, is: 1.645.)

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Your answer should be rounded to 3 decimal places.

Question 6

Is smoking during pregnancy associated with premature births? To investigate this question, researchers selected a random sample of 128 pregnant women who were smokers. The average pregnancy length for this sample of smokers was 257 days. From a large body of research, it is known that length of human pregnancy has a standard deviation of 16 days. The researchers assume that smoking does not affect the variability in pregnancy length.

Find the 95% confidence interval to estimate the length of pregnancy for women who smoke.

(Note: The critical z-value to use, zc, is: 1.960)

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Your answer should be rounded to 3 decimal places.

Answer 1

Solution :

Given that mean x = 3.69 , standard deviation σ = 3.56 , n = 55

=> For 99% confidence interval, Z = 2.58

=> A 99% confidence interval of the mean is

=> x +/- Z*σ/sqrt(n)

=> 3.69 +/- 2.58*3.56/sqrt(55)

=> (2.4515 , 4.9285)

=> (2.45 , 4.93) (rounded)

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5. Solution :

Given that mean x = 487 , standard deviation σ = 100 , n = 695

=> For 90% confidence interval, Z = 1.645

=> A 90% confidence interval of the mean is

=> x +/- Z*σ/sqrt(n)

=> 487 +/- 1.645*100/sqrt(695)

=> (480.7602 , 493.2398)

=> (480.760 , 493.240) (rounded)

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6. Solution :

Given that mean x = 257 , standard deviation σ = 16 , n = 128

=> For 95% confidence interval, Z = 1.960

=> A 95% confidence interval of the mean is

=> x +/- Z*σ/sqrt(n)

=> 257 +/- 1.960*16/sqrt(128)

=> (254.2281 , 259.7719)

=> (254.228 , 259.772) (rounded)