In a study, a random sample of 20 patients was selected to estimate the average recovery time after a surgical procedure. The sample mean recovery time was 10 days, and the sample standard deviation was 2 days. If the population standard deviation is unknown, what should be used to estimate the population mean?a.z statisticb.t statisticc.F statisticd.Chi square tes

When is the z-statistic used to estimate the population mean?a.When the population standard deviation is knownb.When the population standard deviation is unknownc.When the sample size is smalld.When the sample size is large

You are a data analyst for a health insurance company and want to estimate the population mean of the surgery durations for all brain tumor patients. To do so, you select a random sample of 32 brain tumor surgery patients, and you record the surgery duration for each. Assume it is known that the population standard deviation of the durations of all brain tumor surgeries is 1.68 hours.Based on your sample, follow the steps below to construct a 95% confidence interval for the population mean of the surgery durations for all brain tumor patients. (If necessary, consult a list of formulas.)(a)Click on "Take Sample" to see the results from your random sample of 32 brain tumor patients.Take SampleNumber of patients Sample mean Sample standard deviationPopulation standard deviation1.68Enter the values of the sample size, the point estimate for the population mean, the population standard deviation, and the critical value you need for your 95% confidence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select "Compute".Confidence level Critical value99% =z0.0052.57695% =z0.0251.96090% =z0.0501.645Sample size:Point estimate:Population standard deviation:Critical value:ComputeStandard error:Margin of error:95% confidence interval:(b)Based on your sample, enter the lower and upper limits to graph the 95% confidence interval for the population mean of the surgery durations for all brain tumor patients.95% confidence interval:0.002.004.006.008.0010.00

Consider a population with a population standard deviation of 10.6. In order to compute an interval estimate for the population mean, a sample of 42 observations is drawn. (You may find it useful to reference the z table.)a. Is the condition that x̄ is normally distributed satisfied?multiple choice 1YesNo

A population's standard deviation is 12. We want to estimate the population mean with a margin of error of 2, with a 95% level of confidence. (Use t Distribution Table & z Distribution Table.)How large a sample is required? (Round your intermediate calculations to 2 decimal places and round up your answer to the next whole number.)

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. Assuming a population standard deviation of twenty three hours, what is the required sample size if the error should be less than three hours with a 95% level of confidence?