sample final sol

Statistics 13B Spring 2010 Sample Final MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A candy company claims that its jelly bean mix contains 21% blue jelly beans. Suppose that the candies are packaged at random in small bags containing about 400 jelly beans. Describe the sampling distribution model of the proportion of blue jelly beans in a bag. A) mean = 21%; standard error = 2.0% B) There is not enough information to describe the distribution. C) mean = 79%; standard error = 0.8% D) mean = 21%; standard error = 0.8% E) mean = 79%; standard error = 2.0% 2) Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $32,000 and a standard deviation of $3000. If 100 teachers are randomly selected, find the probability that their mean salary is greater than $32,500. A) 0.0950 B) 0.0475 C) 0.9525 D) 0.3312 E) 0.1312 3) When determining the sample size for estimating a population proportion for a given level of confidence and a desired margin of error, the closer to 0.50 that p is estimated to be. A) has an undeterminable effect on the sample size required. B) the smaller the sample size required. C) the larger the sample size required. D) has no effect on the sample size required. E) the farther from 0.50 that 1 - p is estimated to be. 4) The width of a confidence interval estimate for a proportion will be A) narrower when the sample proportion is 0.10 than when the sample proportion is 0.45. B) wider for 90% confidence than for 95% confidence. C) narrowest when the sample proportion is 0.5. D) narrower for a sample size of 50 than for a sample size of 100. E) wider when the sample proportion is 0.95 than when the sample proportion is 0.55. 5) In monitoring lead in the air after an explosion at a battery factory, it is found that measured amounts of lead (in ug/m3) in a 6 days period had a standard error of 1.91. Find the margin of error that corresponds to a 95% confidence interval. A) 95 B) 1.91 C) 3.74 D) 5.65 E) None of the above 6) A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.3%, 5.1%). What is the point estimate of the mean percentage of reservations that are canceled on the day of the flight? A) 1.90% B) 3.20% C) 2.55% D) 5.10% E) 3.80% 7) In a poll of 390 voters in a certain city, 77% said that they backed a bill which would limit growth and development in their city. The margin of error in the poll was reported as 5 percentage points (with a 95% degree of confidence). Which statement is correct? A) There is not enough information to determine whether the margin of error is consistent with the sample size. B) The reported margin of error is consistent with the sample size. C) The sample size is too large to achieve the stated margin of error. D) The stated margin of error could be achieved with a smaller sample size. E) The sample size is too small to achieve the stated margin of error. 8) Using t-tables, report the t-score for the 99% confidence interval with df = 24. A) 2.807 B) 2.492 C) 1.711 D) 2.797 E) 2.779 8) In a survey of 3200 T.V. viewers, 20% said they watch network news programs. Find the standard error for the sample proportion. A) 0.0071 B) 0.0865 C) 0.0721 D) 0.0142 E) 0.0649 9) Of 369 randomly selected medical students, 23 said that they planned to work in a rural community. Construct a 95% confidence interval for the percentage of all medical students who plan to work in a rural community. A) (3.77%, 9.47%) B) (3.30%, 9.17%) C) (3.77%, 8.70%) D) (2.99%, 9.47%) E) (4.16%, 8.30%) 10) How much sugar do reduced sugar cookies typically have? You take a random sample of 51 reduced-sugar cookies and test them in a lab, finding a mean sugar content of 3.2 grams and a standard deviation of 1.1 grams of sugar. Create a 99% confidence interval for the mean grams of sugar. A) (3.1422, 3.2577) B) (2.8032, 3.5968) C) (2.100, 4.300) D) (2.7875, 3.6125) E) (2.7810, 3.6169) 11) Analysis of a random sample of 250 Virginia nurses produced a 95% confidence interval for the mean annual salary of A) If we took many random samples of Virginia nurses, about 95% of them would produce this confidence interval. B) About 95% of Virginia nurses earn between $42,838 and $49,691. C) About 95% of the nurses surveyed earn between $42,838 and $49,691. D) 95% of all nurses earn between $42,838 and $49,691. E) We are 95% confident that the interval from $42,838 to $49,691 contains the true mean salary of all Virginia nurses. 12) A researcher claims that 62% of voters favor gun control. Determine the null and alternative hypotheses. A) Ho: p ? 0.62 vs. Ha: p = 0.62 B) Ho: p ? 0.62 vs. Ha: p < 0.62 C) Ho: p = 0.62 vs. Ha: p ? 0.62 D) Ho: p < 0.62 vs. Ha: p ? 0.62 E) Ho: p = 0.62 vs. Ha: p ? 0.62 13) In a sample of 150 children selected randomly from one town, it is found that 24 of them suffer from asthma. Find the P-value for a test of the claim that the proportion of all children in the town who suffer from asthma is equal to 11%. (the alternative is right-tailed). A) 0.05 B) 0.95 C) 0.01 D) 0.025 E) 0.975 14) Test the claim that for the population of female college students, the mean weight is given by = 132 lb. Sample data are summarized as n = 20, x = 137 lb, and s = 14.2 lb. Find the test statistic. A) 1.729 B)20 C) 1.57 D)14.2 E)-1.57 15) Failing to reject a false Ho: A) is a Type I error. B) has probability 1 - ? of occurring. C) is a Type II error. D) has probability ? of occurring. E) is a correct decision 16) At one school, the average amount of time that ninth-graders spend watching television each week is 21.6 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a significance test to determine whether the average amount of time spent watching television per week has decreased from the previous mean of 21.6 hours. Which type of the significance test should be used? A) Left-tailed B) Right-tailed C)Middle-tailed D) Two-tailed E) Neither 17) 410 people were asked if they were satisfied with their jobs. 37% said they were. It is wished to test the following null hypothesis: Ho: p = 0.3. Find the test statistic. A) 4.125 B) 0.037 C) 0.153 D) 2.612 E) 3.093 18) Given Ha: p ? p0. What is the P-value if the test statistics is calculated to be z = 1.08? A) 0.28 B) 0.58 C) 0.11 D) 0.05 E) 0.22 19) An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for fathers in the town of Cheraw. A random sample of 233 fathers from Cheraw yielded 96 who did not help with child care. Do the data provide sufficient evidence to conclude that in Littleton the proportion is higher than 0.34? Use a 0.05 significance level. Ho: p = 0.34, Ha: p > 0.34; ? = 0.05. Test statistic: z = 2.32. P-Value = 0.0102. State your conclusion in terms of the null hypothesis. A) Do not reject Ho. B) Do not reject Ha. C) Reject H0.34. D) Reject Ho. E) Accept Ho. 20) From the statistics given below, find the value of the point estimate for the difference in proportions n1 = 216, x1 = 76, n2 = 186, x2 = 99 A) 0.392 B) 0.180 C) 0.435 D) 0.308 E) 0.218 21) The U.S. Department of Labor and Statistics wanted to compare the results of an unemployment program for the past two months in the U.S. Suppose the proportion of the unemployed two months ago is p2 and the proportion of the unemployed one month ago is p1. A study found a 99% confidence interval for p2 – p1 is (-0.0012, 0.003). Give an interpretation of this confidence interval. A) We are 99% confident that the proportion of the unemployed one month ago is between 0.12% less and 0.3% more than the proportion of the unemployed two months ago. B) We are 99% confident that the proportion of the unemployed two months ago is between 0.12% less and 0.3% more than the proportion of the unemployed one month ago. C) We know that 99% of the unemployed two months ago is between 0.12% less and 0.3% more than the unemployed one month ago. D) We know that 99% of all random samples done on the population will show that the proportion of the unemployed two months ago is between 0.12% less and 0.3% more than the proportion of the unemployed one month ago. E) We know that 99% of the unemployed one month ago is between 0.12% less and 0.3% more than the unemployed two months ago. 22) A two-sided significance test for two population proportions is to be performed using the P-value approach. Ho: p1 - p2 = 0, Ha: p1 - p2 ? 0 . Use the given sample data to find the P-value for the significance test. Give an interpretation of the P-value. n1 = 200, = 0.10, n2 = 200, = 0.08. A) P-value = 0.2119; If there is no difference in the proportions, there is about a 21.19% chance of seeing the observed difference or larger by natural sampling variation. B) P-value = 0.4238; There is about a 42.38% chance that the two proportions are equal. C) P-value = 0.484; If there is a difference in the proportions, there is a 48.4% chance of seeing the observed difference by natural sampling variation. D) P-value = 0.484; If there is no difference in the proportions, there is about a 48.4% chance of seeing the observed difference or larger by natural sampling variation. E) P-value = 0.2119; There is about a 21.19% chance that the two proportions are equal 23) A researcher is interested in the academic performance differences between individuals using an optimistic versus a pessimistic approach to their studies. If the researcher fails to find a significant difference, when in fact one exists in the population: A) the null hypothesis was correctly accepted. B) the null hypothesis was correctly rejected. C) the research hypothesis was correctly accepted. D) a Type 2 error has been made. E) a Type 1 error has been made. 24) A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet. Use the sample data below to construct a 99% confidence interval for 1 - 2 where 1 and 2 represent the means for the treatment group and the control group respectively. Treatment Group: n = 85, x = 189.1, s = 38.7 Control Group: n = 75, x = 203.7, s = 39.2 A) (-30.5, 1.3) B) (-29.0, -0.2) C)(-1.3, 30.5) D) (-1.5, 30.7) E) (-26.8, -2.4) 25) Refer to Problem 24. Assume that the assumptions and conditions for inference with a two-sample t-test are met. Test the claim that the treatment population mean 1 is smaller than the control population mean 2. Test the claim using a significance level of 0.01. State your conclusion. A) Reject Ho. B) Reject Ha. C) Do not reject Ho. D) Do not reject Ha. E) The control group should be changed. 26) One hundred sixty students who were majoring in either math or English were asked a test question. The researcher recorded whether they answered the question correctly. The response and the major are independent. The results are shown in the table. Accuracy Proportion Calculate the 98% confidence interval for (pmath – pEnglish ) A) (.352, .463) B) (-.703,-.352) C) (-.409, -.703) D) (.503, .708) E) (-.323, -.077) 27) The central limit theorem states that the sampling distribution of x1 – x2 is (approximately) normal. A) when at least one of the sample sizes is greater than or equal to 30. B) when the total number sampled is greater than or equal to 30. C) when either one of the sample sizes is greater than or equal to 30. D) regardless of both of the sample sizes. E) when both of the sample sizes are greater than or equal to 30. 28) In a poll of 278 voters in a certain city, 67% said that they backed a bill which would limit growth and development in their city. The margin of error in the poll was reported as 5.5 percentage points (rounded, 95% confidence level, z=1.96). Which statement is correct? A) The reported margin of error is consistent with the sample size. B) There is not enough information to determine the margin of error. C) For the given sample size, the margin of error should be much larger than stated. D) The sample size is too small to achieve a margin of error less than 10%. E) For the given sample size, the margin of error should be much smaller than stated. 29) 350 randomly selected students took the statistics final. If the margin of error for a 99% confidence interval is 4.45, and the sample mean is 86 (with the standard deviation 12.2), identify the correct lower limit of a 98% confidence interval for the mean score of all students. A) 84.32 B) 89.2 C) 84.48 D) 73.86 E) 83.98 30) Find the standard deviation for the number of people who like to drive fast for a group of n=29, if it is known that the probability is 0.48 that a randomly selected person says that he/she likes to drive fast. A) 13.92 B) 7.2384 C) 3.24 D) 2.690 E) 0.093 31) Assume that the weights of newborn babies are normally distributed with a mean of 6 pounds and a standard deviation of 1.2 pounds. If 20 newborn babies are randomly selected from this population, find the z-score of an average weight of = 6.7 pounds. A) -1.667 B) 2.608 C) 2.61 D) 0.58 E) -2.33 32) Which of the following is a property of the correlation coefficient, r? A) The closer r is to zero, the weaker the linear relationship between x and y. B) r measures the strength of any kind of relationship between x and y. C) r depends on which variable is treated as the response variable. D) r is always between 0 and 1. E) r depends on the units of y or x. 33) Let a sample consist of the following observations: 0.9 0.8 0.1 0.2 0.3 0.5 0.3. Find the mean value. A) 0.3875 B) 0.30 C) 3.1 D) 0.443 E) 0.043 34) The expression P(A ? B) = P(A)P(B|A) is valid if A) A and B are dependent. B) A and B are independent. C) for any events A and B. D) only if A equals BC. E) A and B are mutually exclusive. 35) The following results were obtained from a regression; ? = 5 – 6.2x, r = 0.92, Sx = 4, Sy= 30,= 13, Find . A) 14.24 B) 13.8 C) -1.29 D) 0.23 E) 5.43 36) Probability that a girl learns to read by the age of 3 is 0.78. Probability that a girl learns to read by the age of 4 is 0.34. If a second child is born into a family, what is the probability that this child will learn to read by age of 4 and is a girl? A) 0.68 B) 0.39 C) 0.17 D) 0.085 E) 0.34 37) The table below describes the anxiety level of freshman in high school. High Medium Low Total Men 121 53 22 196 Women 152 98 12 262 Total 273 151 34 458 What is the probability that a freshman in high school has medium anxiety? A) 0.116 B) 0.214 C) 0.596 D) 0.074 E) 0.330 TRUE/FALSE. Mark ‘A’ if the statement is True and 'B' if the statement is False on your scantron. T 38) If p-value of the test statistic is smaller than , conclude ‘Reject Ho’. T 39) For a given level of significance, increasing the sample size will always decrease the probability of committing a Type I error. F 40) The actual P-value is less informative than reporting the result of the test as “Reject Ho” versus “Do Not Reject Ho”. F 41) If the P-value of the test statistic was found to be 0.9 for testing Ho: p = 0.8 against Ha: p < 0.8, then the correct conclusion is ‘there is strong evidence that p < 0.8’. F 42) The goal of the hypothesis test is to prove the null hypothesis. F 43) A hypothesis test is significant when the P-value is greater than ? (=P(type II error). F 44) When the confidence intervals for 1 – 2 contains zero, it is possible to predict which population mean is equal to zero. T 45) However small the difference between two population proportions, for sufficiently large sample sizes, the null hypothesis of equal population proportions is likely to be rejected. T 46) If a test rejects Ho: 1 = 2, then the confidence interval for (1 – 2) having the same error probability does not contain zero. F 47) For two estimates from independent samples, the standard error is T 48) X is distributed as a Binomial(n=7, p=0.52), then P(X = 3.4) = 0. F 49) A point estimate alone is less informative because it tells us how close the estimate is likely to be to the parameter. T 50) A probability distribution specifies the possible probabilities for the outcome values of a random variable. F 51) The normal distribution it is symmetric, whereas t-distribution is not because it depends on the degrees of freedom. T 52) Suppose you have obtained a 95% confidence interval for ?. The relationship between precision and confidence level is: Decreasing the sample size will result in a wider confidence interval but will not change the confidence level. F 53) To avoid working late, a quality control analyst simply inspects the first 100 items produced in a day. This technique produces a random sample. F 54) As long as the sample size is large, random sample always will be produced. T 55) A group of volunteers for a clinical trial consists of 88 women and 80 men. 22 of the women and 20 of the men have high blood pressure. High blood pressure and gender are independent. F 56) The binomial distribution requires at least one success. F 57) Disjoint events are independent events. T 58) Some experts estimate that the length of time people live in a house has a mean of 7.2 years and a standard deviation of 2.4 years. You could estimate the probability that 100 people selected at random had lived in their houses for an average of 8 years or more, but you could not estimate the probability that an individual had done so because the Central Limit Theorem says is approximately Normal for large sample sizes, but not for samples of size 1 (individuals). T 59) Confidence intervals for a proportion require a sample large enough so that np and n(1-p) are at least 15. T 60) The sample mean of a sample from a normally distributed population is always normal. T 61) The practical implication of the effect of sample size on the standard error is: the larger the sample size, the smaller the standard error and thus, the closer the sample mean tends to fall to the population mean. T 62) The two properties of a good estimator are 1) unbiased and 2) small standard error. F 63) The population proportion must lie within the range of values defined by the corresponding confidence-interval estimate, regardless of the level of confidence achieved. F 64) The following is true about the t-distribution: it is used to construct confidence intervals for the population mean when the population standard deviation is known. T 65) Suppose you have obtained a 95% confidence interval for ?. The relationship between precision and confidence level is: Decreasing the confidence level to 90% will result in greater precision. F 66) You wish to estimate the mean weight of machine components of a certain type and you require a 92% degree of confidence that the sample mean will be in error by no more than A pilot study showed that the population standard deviation is estimated to be The sample size required is 172.