3. [-13 Points] - UHSTAT511.E.016.DEFECTIVE In each part, use the information given to calculate the standard error of the mean. (Round your answers to one decimal place.) ASK YOUR TEACHER PRACTICE ANOTHER (a) Mean height for a sample of n = 99 women is )7 = 63.4 inches, and the standard deviation is s = 2.5 inches. inches (b) Mean systolic blood pressure for a sample of n = 90 men is E = 120, and the standard deviation is s = 10. (c) Mean systolic blood pressure for a sample of n = 360 men is )_( = 120, and the standard deviation is s = 10. 4. [-12 Points] UHSTATS 11.E.017. ASK YOUR TEACHER PRACI'ICE ANOTHER Suppose a randomly selected sample of n = 49 men has a mean foot length of; = 27.5 cm, and the standard deviation of the sample is 1.5 cm. (a) Calculate the standard error of the sample mean. (Round your answer to the nearest hundredth.) s.e.(x)= cm (b) Complete the following sentence that interprets this value. Over all possible samples of n = 49 from this population, the average difference between the sample mean and the population mean is about cm. 5. [12 Points] UHSTATS 11.E.018. ASK YOUR TEACHER PRACTICE ANOTHER Suppose a randomly selected sample of n = 36 women has a mean foot length of )7\6. [2/5 Points] PREVIOUS ANSWERS UHSTATS 11.E.029.S. ASK YOUR TEACHER PRACTICE ANOTHER Each man in a random sample ofn = 16 men between 30 and 39 years old is asked to do as many sit-ups as they can in one minute. The mean number is E = 27.2, and the standard deviation of the number of sit-ups is s = 8. m use (a) Find the value of the standard error of the sample mean. Write a sentence that interprets this value. O This is the average difference between the sample and population means over all random samples that can be selected from this sample. C) This is the average difference between the sample and population means over all random samples of n = 16 that can be selected from this sample. 0 This is the maximum difference between the sample and population means over all random samples ofn = 16 that can be selected from this sample. 0 This is the maximum difference between the sample and population means over all random samples that can be selected from this sample. V (b) Find a 95% confidence interval for the population mean. (Round your answers to one decimal place.) to sit-ups (c) Write a sentence that interprets the condence interval in the context of this situation. O With 95% confidence, we can estimate that in the population of men represented by this sample that the maximum number of sit-ups is contained within the interval. 0 With 95% confidence, we can estimate that in the population of men represented by this sample that every individual's number of sit-ups is contained within the interval. 0 With 95% confidence, we can estimate that in the population of men represented by this sample that the minimum number of sit-ups is contained within the interval. With 95% confidence, we can estimate that in the population of men represented by this sample that the mean number of sit-ups is contained within the interval. 7. [4/8 Points] I DETAILS I I PREVIOUS ANSWERS UHSTATS 11.E.032.S. Volunteers who had developed a cold within the previous 24 hours were randomized to take either zinc or placebo lozenges every 2 to 3 hours until their cold symptoms were gone. Twenty-ve participants took zinc lozenges, and 23 participants took placebo lozenges. The mean overall duration of symptoms for the zinc lozenge group was 4.5 days, and the standard deviation of overall duration of symptoms was 1.2 days. For the placebo group, the mean overall duration of symptoms was 7.7 days, and the standard deviation was 1.6 days. IA USES (a) Calculate a 95% condence interval for the mean overall duration of symptoms if everyone in the population were to take the zinc lozenges. (Round your answers to two decimal places.) t0 places.) t0 taken. For relatively I MYNOTES I ASKYOURTEACHER II PRACTICEANOTHER days (b) Calculate a 95% condence interval for the mean overall duration of symptoms if everyone in the population were to take the placebo lozenges. (Round your answers to two decimal days (c) On the basis of the intervals computed in parts (a) and (b), is it reasonable to conclude generally that taking zinc lozenges reduces the overall duration of cold symptoms more than if taking a placebo? Explain why you think this is or is not an appropriate conclusion. Yes, it is v y reasonable to conclude that taking zinc lozenges reduces the duration of symptoms. The condence intervals computed in parts (a) and (b) do not overlap v q , so a reasonable conclusion is that in a population of cold sufferers the mean duration of symptoms if zinc lozenges are taken is V than the mean duration if placebo is (d) In their paper, the researchers say that they checked whether it was reasonable to assume that the data were sampled from a normal curve population and decided that it was. How is this relevant to the calculations done in pars (a) and (b)? small v J samples such as these, a necessary condition (in theory) is that the population of measurements has a normal distribution. 8. [-/2 Points] DETAILS UHSTAT5 11.E.035. MY NOTES ASK YOUR TEACHER A randomly selected sample of n = 12 students at a university is asked, "How much did you spend for textbooks this semester?" The responses, in dollars, are the following. 200 175 450 300 350 250 150 200 320 370 404 250 Computer output with a 95% confidence interval for the population mean is shown in the following figure. Use the Empirical Rule to create an interval that estimates the textbook expenses of 95% of the individual students at the university. (Round the answer to the nearest dollar.) $ to $ Variable N Mean StDev SEMean 95.0% Ci spent 12 284.9 96.1 27.7 [223.9,345.0]9. [1/3 Points] PREVIOUS ANSWERS UHSTAT5 11 .E.036. ASK YOUR TEACHER Suppose that a highway safety researcher is studying the design of a highway sign and is interested in the mean maximum distance at which drivers are able to read the sign. The maximum distances (in feet) at which n = 16 drivers can read the sign are as follows. 440 490 600 540 540 600 240 440 360 600 490 400 490 540 440 490 (a) Are the necessary conditions met for computing a confidence interval for the population mean distance? Assume that the sample can be considered to be a random sample from the population of interest. 0 Yes, all of the necessary conditions are met. 0 No, the sample size is too small. 0 No, there is an outlier. G) No, the sample size is too small and there is an outlier. J (b) Estimate the mean maximum distance at which drivers can read the sign. If conditions are not met, make appropriate adjustments. Use a 95% condence interval. (Outliers may be deleted in this case. Round the answers to 1 decimal place.) 11. [4/10 Points] PREVIOUS ANSWERS UHSTAT5 11.E.054.S. ASK YOUR TEACHER PRACTICE ANOTHER Volunteers who had developed a cold within the previous 24 hours were randomized to take either zinc or placebo lozenges every 2 to 3 hours until their cold symptoms were gone. Twenty-five participants took zinc lozenges, and 23 participants took placebo lozenges. For the placebo group, the mean overall duration of symptoms was X1 = 7.3 days, and the standard deviation was 1.5 days. The mean overall duration of symptoms for the zinc lozenge group was ;2 = 4.2 days, and the standard deviation of overall duration of symptoms was 1.4 days. la USE SALT (a) Calculate ;1 )