A coin is tossed 78 times and 38 heads are observed. Would we infer that this is a fair coin? Use a 92% level confidence interval to base your inference. The sample statistic for the proportion of heads is: (3 decimals) The standard error in this estimate is: (3 decimals) The correct 2* value for a 92% level confidence interval is: (3 decimals) The lower limit of the confidence interval is: (3 decimals) The upper limit of the confidence interval is: (3 decimals) Based on this confidence interval, it is -Se|ect a that the coin is fair. How would a 99% confidence interval compare to the 92% you constructed? They would have the same center. The 99% CI would be narrower. The 99% CI would be wider. There is no way to tell how they would compare. They would have different centers. An insurance company nds that of 607 randomly selected auto accidents, teenagers were driving the vehicle in 113 of them. (a) Find the 95% confidence interval for the proportion of auto accidents with teenaged drivers: ( , ) (Use 4 decimals.) (b) What does this inten/al mean? We are 95% condent that a randomly chosen accident with a teenaged driver will fall inside the above interval. We are 95% condent that the percent of accidents with teenaged drivers is 18.6%. We are 95% condent that the proportion of all accidents with teenaged drivers is inside the above interval. We are 95% condent that of the 607 sampled accidents, the proportion with a teenaged driver falls inside the above interval. (c) What does the 95% confidence level mean? We expect that 95% of random samples of size 607 will produce m that contain(s) the --~ of accidents that had teenaged drivers. (d) A politician urging tighter restrictions on drivers' licenses issued to teens says, "One of every ve auto accidents has a teenaged driver." Does the condence interval support or contradict this statement? The confidence interval contradicts the assertion of the politician. The figure quoted by the politician is outside the interval. The confidence interval supports the assertion of the politician. The figure quoted by the politician is outside the interval. The confidence interval supports the assertion of the politician. The figure quoted by the politician is inside the interval. The confidence interval contradicts the assertion of the politician. The figure quoted by the politician is inside the interval. Recently in a large random sample of teens a proportion of 0.8 teens said they send text messages to friends. The margin of error for a 98% confidence interval was 0.028. (a) What is the sample proportion of teens who send text messages to friends? (3 decimal places) (b) Use the information given to find an interval estimate for the population proportion of teens who send text messages to friends. Lower Limit = (3 decimal places) Upper Limit = (3 decimal places) [-l15 Points] 0/3 Submissions Used PRACTICE ANOTHER A random sample of 1200 Freshmen at UGA were asked if they had applied for student football tickets. The proportion who answered yes was 0.84. The standard error of this estimate is 0.011. (a) Find the margin of error for a 95% condence interval for the population proportion who applied for football tickets. (3 decimal places) (b) Construct the 95% confidence interval. Lower Limit (3 decimal places) Upper Limit (3 decimal places) (c) Since the sample was randomly selected, will this confidence interval be valid? None of these. Yes because the sample size is greater than 30. Yes because at least one of (1200)*(0.84) and (1200)*(1 - 0.84) is greater than 15. Yes because both (1200)*(0.84) and (1200)*(1 - 0.84) are greater than 15. Yes because at least one of (1200)*(O.84) and (1200)*(1 - 0.84) is greater than 30. (d) Using the above confidence interval, what can you say about the true population proportion? If we were to take many samples like this, and calculate a 95% confidence interval for each one, approximately 95% of these intervals would contain the true population proportion. We are 95% condent that the sample proportion is in this interval. When a truckload of apples arrives at a packing plant, a random sample of 200 apples are selected and examined for bruises and other defects. In reality, 8% of the apples on a particular truck are bruised or othenNise unsatisfactory. (a) How many standard errors away from 0.08 would you need to go to contain 89% of the sample proportions of bad apples you might expect to find? (3 decimal places) (b) Suppose you were going to construct an 89% confidence interval from this population. What critical value should you use? (3 decimal places) [-/15 Points] 0/3 Submissions Used PRACTICE ANOTHER The 2002 General Social Survey asked, "What do you think is the ideal number of children for a family to have?" The 502 females who responded had a mean of 3.05, and standard deviation of 1.79. The 95% condence interval is (2.89, 3.21). (a) What is the sample statistic? (2 decimal places) (b) Find the standard error. (3 decimal places) (c) Using the confidence interval, what can you say about the true population mean? We are condent that, 95% of the time, the true mean ideal number of children for a family to have is between 2.89 and 3.21. We are 5% confident that the true mean ideal number of children for a family to have is between 2.89 and 3.21. We are condent that 95% of Americans think that the true mean ideal number of children for a family to have is between 2.89 and 3.21. We are 95% confident that the true mean ideal number of children for a family to have is between 2.89 and 3.21. (d) According to this interval, is it plausible that the population mean is 2? Explain. Yes, 2 is not in this interval. No, 2 is not in this interval. No, 2 is in this interval. Yes, 2 is in this interval. (e) If we were to conduct a hypothesis test of H0: )4 = 2 vs. Ha: )4 2, what could we say based off the above interval? The p-value is less than .05 The p-value is greater than .05 None of the other conclusions could be made We would not reject the null hypothesis We would re'ect the null h othesis In order to evaluate the effectiveness of a new type of plant food that was developed for tomatoes, a study was conducted in which a random sample of n = 71 plants received a certain amount of this new type of plant food each week for 14 weeks. The variable of interest is the number of tomatoes produced by each plant in the sample. The table below reports the descriptive statistics for this study: Descriptive statistics for the tomato food study sample Variable n sample mean standard standard error deviation \"umber f 71 40.20 9.60 1.139 tomatoes Assuming the population is normally distributed, the investigators would like to construct a 90% condence interval for the average number of tomatoes that all plants of this variety can produce when fed this supplement like this. a) The margin of error is: (3 decimals) b) The corresponding 90% confidence interval for the true population mean is: Lower Limit: (3 decimals) to Upper Limit: (3 decimals) c) What would we conclude at a = 0.1 for the hypothesis test H0: y = 44.199 vs. Ha: [4 44.199? We have sufficient evidence to conclude that the true mean is different from 44.199. We have enough evidence to conclude that the true mean is 44.199. We do not have enough evidence to conclude the true mean is 44.199. We do not have enough evidence to conclude the true mean is 40.20. We have insufficient evidence to conclude the true mean is different from 44.199. As part of its eco-friendly campaign, a company has asked for your advice whether installing a wind turbine will generate enough electricity to be cost effective. To produce enough electricity, the average wind speed needs to be least 15 mph. Based on historical data from the past 5 years, 43 days were randomly chosen and their wind speed measurements were written down. This resulted in an average wind speed of 18 mph with a standard error of 0.6710 mph. A histogram of these wind speeds yielded a right-skewed shape. (a) Are the conditions met for constructing a confidence interval? (Check all that apply.) The Nearly Normal condition is met. It is reasonable to assume that weather conditions on the various days were independent of each other. The days were randomly chosen. None of the conditions are met. (b) Find the 98% condence interval for the true average wind speed. (Use 4 decimal places) ( I ) (c) Does the above confidence interval provide evidence that a wind turbine would be cost effective? No, since the lower boundary is greater than the required wind speed of 15 mph, there is evidence the true average wind speed is greater than 15 mph. Yes, since the lower boundary is less than the required wind speed of 15 mph, it is possible the true average wind speed is less than 15 mph. Yes, since the lower boundary is greater than the required wind speed of 15 mph, there is evidence the true average wind speed is greater than 15 mph. No, since the lower boundary is less than the required wind speed of 15 mph, it is possible the true average wind speed is less than 15 mph. -/9 Points] DETAILS 0/3 Submissions Used MY NOTES PRACTICE ANOTHER In a certain region, 17% of people over age 50 didn't graduate from high school. We would like to know if this percentage is the same among the 25-30 year age group. Use critical values to exactly 3 decimal places. (a) How many 25-30 year old people should be surveyed in order to estimate the proportion of non-grads to within 5% with 95% condence? (b) Suppose we wanted to cut the margin of error to 3%. How many people should be sampled now? (c) What sample size is required for a margin of error of 6%