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1 Chapter 7 Exam A Name 1) How do you determine whether to use the z or t distribution in computing the margin of error, E = z α/2 σn or E = t α/2 s n? 1) Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. 2) n = 195, x = 162; 95% confidence 2) A) < p < B) < p < C) < p < D) < p < Find the indicated critical z value. 3) Find the value of zα/2 that corresponds to a confidence level of 89.48%. A) 1.25 B) 1.62 C) D) ) Express the confidence interval using the indicated format. 4) Express the confidence interval (0.432, 0.52) in the form of p^ ± E. A) ± B) ± C) ± D) ± ) Solve the problem. 5) Find the critical value χ 2 R corresponding to a sample size of 19 and a confidence level of 99 5) percent. A) B) C) D) ) Describe the steps for finding a confidence interval. 6) Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. 7) 98% confidence; the sample size is 800, of which 40% are successes 7) A) B) C) D) Solve the problem. Round the point estimate to the nearest thousandth. 8) 50 people are selected randomly from a certain population and it is found that 12 people in the sample are over 6 feet tall. What is the point estimate of the proportion of people in the population who are over 6 feet tall? A) 0.76 B) 0.24 C) 0.50 D) ) Copyright 2014 Pearson Education, Inc. 1

2 Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. 9) Of 380 randomly selected medical students, 21 said that they planned to work in a rural 9) community. Find a 95% confidence interval for the true proportion of all medical students who plan to work in a rural community. A) < p < B) < p < C) < p < D) < p < Use the given data to find the minimum sample size required to estimate the population proportion. 10) Margin of error: 0.028; confidence level: 99%; p^ and q^ unknown A) 1116 B) 2223 C) 1939 D) ) Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. 11) 95% confidence; n = 2388, x = ) A) B) C) D) ) Interpret the following 95% confidence interval for mean weekly salaries of shift managers at Guiseppe's Pizza and Pasta < μ < ) 13) Define margin of error. Explain the relation between the confidence interval and the error estimate. Suppose a confidence interval is 9.65 < μ < Find the sample mean x and the error estimate E. 13) 14) Thirty randomly selected students took the calculus final. If the sample mean was 95 and the 14) standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students. A) < μ < B) < μ < C) < μ < D) < μ < Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. 15) A survey of 300 union members in New York State reveals that 112 favor the Republican candidate 15) for governor. Construct the 98% confidence interval for the true population proportion of all New York State union members who favor the Republican candidate. A) < p < B) < p < C) < p < D) < p < Copyright 2014 Pearson Education, Inc. 2

3 16) In constructing a confidence interval for σ or σ2, a table is used to find the critical values χ 2 L and 16) χ 2 R for values of n 101. For larger values of n, χ 2 L and χ 2 R can be approximated by using the following formula: χ2 = 1 2 [± z α/2 + 2k - 1 ] 2 where k is the number of degrees of freedom and zα/2 is the critical z score. Construct the 90% confidence interval for σ using the following sample data: a sample of size n = 232 yields a mean weight of 154 lb and a standard deviation of 25.5 lb. Round the confidence interval limits to the nearest hundredth. A) lb < σ < lb B) lb < σ < lb C) lb < σ < lb D) lb < σ < lb 17) A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was ) milligrams with s = 17.6 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs. A) mg < μ < mg B) mg < μ < mg C) mg < μ < mg D) mg < μ < mg 18) Draw a diagram of the chi-square distribution. Discuss its shape and values. 18) Do one of the following, as appropriate: (a) Find the critical value zα/2, (b) find the critical value tα/2, (c) state that neither the normal nor the t distribution applies. 19) 99%; n = 17; σ is unknown; population appears to be normally distributed. 19) A) tα/2 = B) zα/2 = C) tα/2 = D) zα/2 = ) n = 30, x = 84.6, s = 10.5, 90% confidence 20) A) < μ < B) < μ < C) < μ < D) < μ < ) When determining the sample size needed to achieve a particular error estimate you need to know σ. What are two methods of estimating σ if σ is unknown? 21) Copyright 2014 Pearson Education, Inc. 3

4 22) Identify the correct distribution (z, t, or neither) for each of the following. 22) Find the indicated critical z value. 23) Find the critical value zα/2 that corresponds to a 91% confidence level. A) 1.34 B) C) 1.70 D) ) 24) Bert constructed a confidence interval to estimate the mean weight of students in his class. The population was very small - only 30. Ruth constructed a confidence interval for the mean weight of all adult males in the city. She based her confidence interval on a very small sample of only 5. Which confidence interval is likely to give a better estimate of the mean it is estimating? Which is likely to be more of a problem, a small sample or a small population? 24) Do one of the following, as appropriate: (a) Find the critical value zα/2, (b) find the critical value tα/2, (c) state that neither the normal nor the t distribution applies. 25) 90%; n =9; σ = 4.2; population appears to be very skewed. 25) A) zα/2 = B) zα/2 = C) zα/2 = D) Neither the normal nor the t distribution applies. Copyright 2014 Pearson Education, Inc. 4

5 Answer Key Testname: CHAPTER 7 EXAM A 1) Provided n > 30, the standard normal distribution is the one to use. If n 30, the population must be normal and σ must be known to use the formula. 2) A 3) B 4) A 5) A 6) Begin with the summary statistics for x and s. Determine whether the z or t distribution is required. Compute the error estimate using either E = z α/2 σn or E = t α/2 s. Find the interval using x ± E. Interpret the confidence n interval. 7) C 8) B 9) A 10) D 11) B 12) We are 95% sure that the interval contains the true population value for mean weekly salaries of shift managers at Guiseppe's Pizza and Pasta. 13) The margin of error is the maximum likely difference between the observed sample mean x and the true value for the population mean μ. The confidence interval is found by taking the sample mean x and adding the margin of error E to find the high value and subtracting E to find the low value of the interval. In the interval 9.65 < μ < 11.35, the sample mean x is 10.5 and the error estimate E is ) A 15) C 16) D 17) C 18) The chi-square distribution is non-symmetric and skewed to the right. The values are 0 and positive. 19) C 20) C 21) 1) Use the range rule of thumb. 2) Conduct a pilot study and base your estimate of σ on the first collection of at least 31 randomly selected values. 22) 23) C 24) Bert's confidence interval is likely to give a better estimate. A small sample is more likely to be a problem than a small population. 25) D Copyright 2014 Pearson Education, Inc. 5

1) What is the probability that the random variable has a value less than 3? 1)

1) What is the probability that the random variable has a value less than 3? 1) Ch 6 and 7 Worksheet Disclaimer; The actual exam differs NOTE: ON THIS TEST YOU WILL NEED TO USE TABLES (NOT YOUR CALCULATOR) TO FIND PROBABILITIES UNDER THE NORMAL OR CHI SQUARED OR T DISTRIBUTION! SHORT