2. Out of a sample of 200 gaming systems, 4 units were found to be defective. The industry standard for such systems under normal conditions is three percent defective. We would like to determine, at a 90% confidence interval, if the percentage of defective units is below industry standards. a. State the null and alternative hypotheses. b. Determine the z-score associated with the level of significance a. C. Compute test statistic.
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- What is meant by the sample space of an experiment?3.Michael wants to make a confidence interval estimate for the proportion of community members in favor of a tax increase for more local school funding. If he wants the margin of error to be no more than 0.025 at a 90% confidence level, a)What is the required sample size required to obtain the desired margin of errorAn epidemiologist is worried about the prevalence of the flu in East Vancouver and the potential shortage of vaccines for the area. She will need to provide a recommendation for how to allocate the vaccines appropriately across the city. She takes a simple random sample of 339 people living in East Vancouver and finds that 40 have recently had the flu. For each of the following statements, specify whether the statement is a correct interpretation of the 95% confidence interval for the true proportion of East Vancouver residents who have recently had the flu. A. 11.80% (40/339) of East Vancouver residents have recently had the flu. ? true false B. There is a 95% probability that the true proportion of East Vancouver residents who have recently had the flu equals 40/339. ? true false C. If another random sample of 339 East Vancouver residents is drawn, there is a 95% probability that the sample proportion of East Vancouver residents who have recently had the flu equals 40/339. ?…
- Suppose that a safety group surveyed 1,100 drivers. Among those surveyed, 65% said that careless or aggressive driving was the biggest threat on the road, and 25% said that cell phone usage by other drivers was the driving behavior that annoyed them the most. Based on these data and assuming that the sample was a simple random sample, construct and interpret a 95% confidence interval estimate for the true proportion in the population of all drivers who are annoyed by cell phone users. The confidence interval estimate is ??––––––??> (Round to three decimal places as needed. Use ascending order.) Interpret the confidence interval estimate. A. There is a 0.95 probability that the population proportion of drivers who are annoyed by cell phone users is in the interval. B. There is 95% confidence that the population proportion of drivers who are annoyed by cell phone users is in the interval. C. There is 95% confidence that the population proportion…A survey of entry level corporate analysts in New York City asked, approximately how many hours per week do you work? A) If the population standard deviation is known to be 4.7 hours, and a random sample of 35 analysts yielded a mean of 50.5 hours, then construct a 90% confidence interval for the mean number of hours worked by entry level analysts. B) In the above confidence interval, suppose that we want a margin of error of +/- 1 hour. What sample size would be needed to achieve this? C) As mentioned in class, it is unlikely that the population standard deviation is known. Suppose instead that the sample standard deviation was 4.7 hours. Using the other values from part (a), form a 90% confidence interval for the mean number of hours worked by entry level analysts.The St. Lucie County Health Department needs to estimate the proportion of all children in the county aged 19-35 months that are completely up to date with all state-recommended immunizations. The St. Lucie County Health Department found that 67% of a random sample of children in the county aged 19-35 months were completely up to date with all state-recommended immunizations. Find three different confidence intervals - one with sample size 239, one with sample size 596, and one with sample size 937. Assume that 67% of the children each sample are completely up to date with all state recommended immunizations. Notice how the sample size affects the margin of error and the width of the interval. Report confidence interval solutions using interval notation. Report all solutions in percent form, rounded to two decimal places, if necessary. When n=239n=239, the margin of error for a 97% confidence interval is given b When n=239n=239, a 97% confidence interval is given by When n=596n=596,…
- The St. Lucie County Health Department needs to estimate the proportion of all children in the county aged 19-35 months that are completely up to date with all state-recommended immunizations. The St. Lucie County Health Department found that 67% of a random sample of children in the county aged 19-35 months were completely up to date with all state-recommended immunizations. Find three different confidence intervals - one with sample size 239, one with sample size 596, and one with sample size 937. Assume that 67% of the children each sample are completely up to date with all state recommended immunizations. Notice how the sample size affects the margin of error and the width of the interval. Report confidence interval solutions using interval notation. Report all solutions in percent form, rounded to two decimal places, if necessary. When n=596n=596, a 97% confidence interval is given by= When n=937n=937, the margin of error for a 97% confidence interval is given by= When n=937n=937,…A telephone company has the business objective of wanting to estimate the proportion of households that would purchase an additional telephone line if it were made available at a reduced installation cost. Data is collected from a random sample of 500 households. The results indicate that 135 of the households would purchase the additional telephone line at a reduced installation cost. - construct a ninety nine percent confidence interval estimate for the population proportion of households that would purchase the additional telephone line.The Okeechobee County Economic Development Board needs to estimate the proportion of all county residents who have earned at least a bachelor's degree. A random sample conducted by the Okeechobee County Economic Development Board found that 10.5% of all county residents held at least a bachelor's degree.Find three different confidence intervals - one with sample size 180, one with sample size 451, and one with sample size 621. Assume that 10.5% of the county residents in each sample have earned at least a bachelor's degree. Notice how the sample size affects the margin of error and the width of the interval.Report confidence interval solutions using interval notation. Report all solutions in percent form, rounded to two decimal places, if necessary. When n=180n=180, the margin of error for a 95% confidence interval is given by .When n=180n=180, a 95% confidence interval is given by . When n=451n=451, the margin of error for a 95% confidence interval is given by .When n=451n=451, a…
- After reporting the results from a formal hypothesis test, it is often likely that statisticians will report a confidence interval in order to indicate that a null value is present, indicating a significant response . True FalseThe National Weight Control Registry tries to mine secrets of success from people who lost at least 30 pounds and kept it off for at least a year. It reports that out of 2,720 registrants, 439 were on a low-carbohydrate diet (less than 90 grams a day). a. Develop a 95% confidence interval for the proportion of people on a low-carbohydrate diet.b. Is it possible that the population percentage is 16%? c. How large a sample is needed to estimate the proportion within 0.55%?A 90 percent confidence interval is to be created to estimate the proportion of television viewers in a certain areawho favor moving the broadcast of the late weeknight news to an hour earlier than it is currently. Initially, theconfidence interval will be created using a simple random sample of 9,000 viewers in the area. Assuming that thesample proportion does not change, what would be the relationship between the width of the original confidenceinterval and the width of a second 90 percent confidence interval that is created based on a sample of only 1,000viewers in the area?(A) The second confidence interval would be 9 times as wide as the original confidence interval.(B) The second confidence interval would be 3 times as wide as the original confidence interval.(C) The width of the second confidence interval would be equal to the width of the original confidence interval.(D) The second confidence interval would be 1/3 as wide as the original confidence interval.(E) The second…