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Descriptive statistics, Confidence Interval & Sample size

# 16
A random sample of the number of farms (in thousands) in various states follows. Estimate the mean of farms per state with 90% confidence.

47 95 54 33 64 4 8 57 9 80
8 90 3 49 4 44 79 80 48 16
68 7 15 21 52 6 78 109 40 50

Answer -

A pizza shop owner wishes to find the 95% confidence interval of the true mean cost of a large plain pizza. How large should the sample be if she wishes to be accurate to within $0.15? A previous study showed that the standard deviation of the price was $0.26.

Answer -

The daily salaries of substitute teachers for eight local school districts is shown. What is the point estimate for the mean? Find the 90% confidence interval of the mean for the salaries of substitute teachers in the region.
90 56 60 55 70 55 60 55


A study by the University of Michigan found that one in five 13- and 14-year-olds in a sometime smoker. To see how the smoking rate of the student at a large school district compared to the national rate, the superintendent surveyed two hundred 13- and 14-year-old students. Find
the 99% confidence interval of the true proportion, and compare this with the University of Michigan study.


Obesity is defined as a body mass index (BMI) of 3 kg/m2 or more. A 95% confidence interval for the percentage of U.S. adults aged 20 years and over who were obese was found to be 22.4% to 23.5%. What was the sample size?


A random sample of stock prices per share (in dollars) is shown. Find the 90% confidence interval for the variance and standard deviation for the prices. Assume the variable is normally distributed.

26.69 13.88 28.37 12.00
75.37 7.50 47.50 43.00
3.81 53.81 13.62 45.12
6.94 28.25 28.00 60.50
40.25 10.87 46.12 14.75


1. Give the type of distribution pattern that occurs when the majority of the data values fall to the left of the mean?
A) symmetrical
B) positively skewed
C) negatively skewed
D) left skewed

2. Which of the following properties does not apply to a theoretical normal distribution?
A) The normal distribution is bell-shaped.
B) The mean, median, and mode are equal.
C) The normal distribution is bimodal.
D) The curve never touches the x-axis.

3. Find the probability P(Z < 0.37) using the standard normal distribution.

6. In order to be accepted into a top university, applicants must score within the top 5% on the SAT exam. Given that the test has a mean of 1000 and a standard deviation of 200, what is the lowest possible score a student needs to qualify for acceptance into the university?
A) 1330
B) 1400
C) 1250
D) 1100

8. If the standard deviation of a population is 20 and we take a sample of size 4, then the standard error (the standard deviation of the sample mean) is
A) 10.00
B) 2.00
C) 40.00
D) 5.00

11. A lawyer researched the average number of years served by 45 different justices on the Supreme Court. The average number of years served was 13.8 years with a standard deviation of 7.3 years. What is the 95% confidence interval for the average number of years served by all Supreme Court justices?

13. In a study of size 8 where the variance is unknown, the distribution that should be used to calculate confidence intervals is
A) a normal distribution
B) a t distribution with 7 degrees of freedom
C) a t distribution with 8 degrees of freedom
D) a t distribution with 9 degrees of freedom

14. What is the 90% confidence interval for the variance of exam scores for 28 algebra students, if the standard deviation of their last exam was 12.7?

15. The value for for a 99% confidence interval when is 9.262.
A) True
B) False

17. A recent poll of 700 people who work indoors found that 278 of them smoke. If the researchers want to be 98% confident of their results to within 3.5%, how large a sample is necessary?
A) 751
B) 1062
C) 1301
D) 532

Solution Summary

The solution provides step by step method for the calculation of confidence interval for population mean, sample size and arithmetic mean. Formula for the calculation and Interpretations of the results are also included.