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elem. stat. week 5 quiz

# elem. stat. week 5 quiz - ue’d 3:3pm Course Math 201 Fall...

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Unformatted text preview: ue’d: 09/26/11 3:3pm Course: Math 201 Fall B10 Book: Larson: Elementary Statistics: Picturing the World, 5e Assignment: Week 5 Quiz A machine used to ﬁll gallon—sized paint cans is regulated so that the amount of paint dispensed has a mean of 134 ounces and a standard deviation of 0.40 ounce. You randomly select 35 cans and carefully measure the contents. The sample mean of the cans is 133.9 ounces. Does the machine need to be reset? Explain your reasoning. N0 , it is likely that you would have randomly sampled 35 cans with a mean equal to 133.9 ounces, because it lies within the range of a usual event, namely within 2 standard deviations of the mean of the sample means. Find the margin of error for the given values of c, s, and n. c=0.90, s:3.3,n=64 E I .679 A doctor wants to estimate the HDL cholesterol of all 20— to 29-year—old females. How many subjects are needed to estimate the HDL cholesterol within 2 points with 99% conﬁdence assuming 6 I 18.]? Suppose the doctor would be content with 95% conﬁdence. How does the decrease in conﬁdence affect the sample size required? A 99% conﬁdence level requires 544 subjects. ﬁllx A 95% conﬁdence level requires 315 subjects. How does the decrease in conﬁdence affect the sample size required? The sample size is the same for all levels of conﬁdence. g The lower the conﬁdence level the smaller the sample size. The lower the conﬁdence level the larger the sample size. YOU ANSWERED: 541/; ,- 2 l "7 ’F E i i fr“ 4 - t if a ‘ 2‘ [1-42 : i ./ J ! «W«~_me. » “a MM " Page 1 r . m, _ , Assignment: Week 5 Quiz Submitted: 09/26/11 3:33pm Course: Math 201 Fall B10 Book: Larson: Elementary Statistics: Picturing the World, 5e ‘ A researcher wishes to estimate, with 90% conﬁdence, the proportion of adults who have / high-speed Internet access. Her estimate must be accurate within 2% of the true proportion. a) Find the minimum sample size needed, using a prior study that found that 52% of the respondents said they have high—speed Internet access. b) No preliminary estimate is available. Find the minimum sample size needed. a) What is the minimum sample size needed using a prior study that found that 52% of the respondents said they have high-speed Internet access? . I 52(- l] ' )[ I . [I ‘16" Z I . 105/ Z i - 015 697 11 : 1689 I s..— b) What is the minimum sample size needed assuming that no preliminary estimate is available? 11 = 1692 YOU ANSWERED: 422 In a survey of 7000 women, 4431 say they change their nail polish once a week. Construct a 95% conﬁdence interval for the population proportion of women who change their nail polish once a week. A 95% conﬁdence interval for the population proportion is ( .622 , .644 The mean height of women in a country (ages 20 — 29) is 64.1 inches. A random sample of 65 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume G = 2.77. The probability that the mean height for the sample is greater than 65 inches is 0.0044 . YOU ANSWERED: .3 Page 2 Submitted: 09/26/11 3:33pm Assignment: Week 5 Quiz Course: Math 201 Fall B10 Book: Larson: Elementary Statistics: Picturing the World, 5e The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. For a sample of n = 75, ﬁnd the probability of a sample mean being greater than 216 if u = 215 and 6 : 3.9. For a sample of n = 75, the probability of a sample mean being greater than 216 if u = 215 and o I 3.9 is 0.0132 .> If— Would the given sample mean be considered unusual? The sample mean would be considered unusual because it does not lie within the range of a usual event, namely within 2 standard deviations of the mean of the sample means. YOU ANSWERED: .225 lies In a random sample of four microwave ovens, the mean repair cost was \$65.00 and the standard deviation was \$1 1.50. Assume the variable is normally distributed and use a t-distribution to construct a 90% conﬁdence interval for the population mean 11. What is the margin of error of u? The 90% conﬁdence interval for the population mean u is (51.47 , 78.53 The margin of error is 13.53 . YOU ANSWERED: 52.74 77.26 12.26 Use the conﬁdence interval to ﬁnd the estimated margin of error. Then ﬁnd the sample mean. A biologist reports a conﬁdence interval of (2.5,3.3) when estimating the mean height (in centimeters) of a sample of seedlings. The estimated margin of error is .4 . The sample mean is 2.9 . Find the critical value t c for the conﬁdence level 0 : 0.80 and sample size n = 15. tc : 1.345 Page 3 Assignment: Week 5 Quiz Submitted: 09/26/11 3:33pm Course: Math 201 Fall B1 Book: Larson: Elementary Statistics: Picturing the World, Se Let p be the population proportion for the following condition. Find the point estimates for p and q. A study of 4348 adults from country A found. that 2488 were obeSe or overweight. The point estimate for p, 3, is .572 . The point estimate for q, a, is .428 . You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and 95% conﬁdence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the conﬁdence intervals. A random sample of 35 gas grills has a mean price of \$631.40 and a standard deviation of \$59.40. The 90% conﬁdence interval is (614.88 , 647.92 The 95% conﬁdence interval is (611.72 , 651.08 Which interval is wider? Choose the correct answer below. a The 90% conﬁdence interval The 95% conﬁdence interval Page 4 Assignment: Week 5 Quiz Submitted: 09/26/11 3:33pm Course: Math 201 Fall B10 Book: Larson: Elementary Statistics: Picturing the World, 5c The state test scores for 12 randomly selected high school _ 1429 1226 98 5 seniors are shown on the right. 691 721 837 723 743 545 627 1443 944 Assume the population is normally distributed. (a) Find the sample mean. §= 909.5 (b) Find the sample standard deviation. 5 = 305.3 (0) Construct a 95% conﬁdence interval for the population mean a. A 95% conﬁdence interval for the population mean is ( 715.5 , 1103.5 YOU ANSWERED: 9.0 3.28 14.72 A population has a mean [,1 I 88 and a standard deviation 6 I 14. Find the mean and standard deviation of a sampling distribution of sample means with sample size n : 49. Page 5 ...
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elem. stat. week 5 quiz - ue’d 3:3pm Course Math 201 Fall...

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