In order to determine the public opinion for converting an industrial area into a public park a poll has been conducted. 32 out of 40 people support the park. (a) Based on this sample construct a 88% confidence interval for the support. b) If the true public support is 90%, how would you explain the result obtained from the confidence interval? Explain in relation to the confidence level. =) What sample size is needed to obtain an 88% confidence interval such that half the width is 0.047
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- What is meant by the sample space of an experiment?An insurance company reported that, on average, claims for a certain medical procedure are $942. An independent organization constructed a 95% confidence interval of ($930 , $950) for the average amount claimed for the particular medical procedure. What conclusion best evaluates the truthfulness of the number reported by the insurance company? a) With 95% certainty, the average claim for this medical procedure is $942.b) With 95% certainty, the average claim for this medical procedure is not $942.c) The confidence interval is consistent with an average claim of $942 for this medical procedure.d) With 100% certainty, the average claim for this medical procedure is $942A consumer magazine polls cell-phone-users to see if they are happy with their phones and would purchase the same model again. They randomly selected cell-phone-users and found the following: 429 of 550 owners of iPhones would purchase their phone again, and 324 of 450 owners of Androids would purchase the same phone again. a) Check the assumptions and conditions for comparing proportions.b) Find a 95% confidence interval (Two-Proportion z-Interval) for the difference in the proportions.c) Interpret your interval in the context of the problem. What does the confidence interval say about the difference in the satisfaction of the two types of owners (hint: pay attention to the signs on the LB & UB)?d) Conduct a hypothesis test with an alpha-level of 0.05 to determine if there is strong evidence that owners of iPhones are happier with their purchase than owners of Androids. (Be sure to give the name of the test that you are performing.)e) If your conclusion was wrong, what type of…
- The results of the National Health and Nutrition Examination Survey for the year 2011-12 found that 12.9% of the adults of age 20 and more in the United States had high total cholesterol. Assume that a researcher surveys a sample size of 120 for above 20 years. Construct a 95% confidence interval estimate for the population proportion so that the cholesterol level is the same as 12.9% (PHStat). Assume that a researcher surveys a sample size of 1,200 for more than 20 years. Construct a 95% confidence interval estimate for the population proportion so that the cholesterol level is the same as 12.9%.(PHStat) Compare the results in (a) and (b).A students wants to estimate the proportion of professors who drive pickup trucks. She surveys 250 professors from across the country and uses the results to construct a 90% confidence interval estimate of p, the proportion of all professors who drive pickup trucks. If she were to do this with a total of 111 different sample of 250 professors, yielding 111 different 90% confidence interval estimates of p, approximately how many intervals would contain the true value of pA college lecturer randomly selected thirty-five students in his class to complete an assigned task and it is found that the 95% confidence interval for the true average time in completing the task is (17.278, 28.722) minutes. It is thought that this interval is too wide, and a confidence interval of total width 5 minutes will be more desirable. (a) Using the same value of ?, find the new confidence interval in this case.(b) Find the confidence level for the interval in part (a).
- A sample of 250 items from lot A contains 10 defective items, and a sample of 300 itemsfrom lot B is found to contain 18 defective items. Construct a 98% confidence interval for the difference of proportions of defective items.In order to estimate the overall proportion of students who favor a shorter semester system, we selected a simple random sample of 36 students and found that 24 of them favor a shorter semester system.(a) Construct a 90% confidence interval for the overall proportion of students who favor a shorter semester system.(b) Find the margin of error associated with this c.i. and interpret the answer in plain language.(c) In order for the margin of error to be no greater than 0.1 (or 10 percentage points), how large a sample should be drawn instead?The owner had a goal of acheiving a per sale amount of 110 euro for all sales made on February 14. Based on the inference carried out so far, do you think she may be disappointed? a. Yes, because the sample mean estimated from this sample was less than 110 euro. b. Yes, because the value 110 euro is not contained in the confidence interval and is therefore not a likely value for the mean sale amount. c. No, because the value 110 euro is contained in the confidence interval and therefore could be a possible value for the mean sale amount.
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