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1. (Sampling distribution & confidence interval) A random variable has a population mean equal to 1,573 and population variance equal to 952,021. Your interest lies in estimating the population mean of this random variable. (Of course, you do not know what the population mean and population variance are.) With that in mind, you take a representative sample of size 85 from the population of the random variable. You then use this sample data to calculate the sample average as an estimate for the population mean.
a) Using your knowledge about the central limit theorem (CLT), and assuming that the CLT has already "established itself" / "kicked in" when the sample size is 85, what is the probability that the sample average that you calculated will lie between 1,502 and 1,748?
b) You then use your sample data to calculate a 92% confidence interval for the population mean. Assuming that you can estimate the variance of the underlying random variable very precisely with your sample data, what should be the width of this confidence interval?
c) Suppose that now you would like to cut the width of your 92% confidence interval in half by increasing your sample size. What should be the size of your sample in order to achieve this goal?
Second treatment had M = 52 with s^2 = 36. Do these data point to significant difference between two treatments? Use the two-tailed test with α = .05.
Hanna Properties specializes in custom-home resales in the Equestrian Estates, an exclusive subdivision in Phoenix, Arizona. A random sample of nine custom homes currently listed for sale provided the following information on size and price.
A sample of 10 electronic tubes produced by a company showed a mean lifetime of 1200 hours and a standard deviation of 100 hours. estimate the mean and the standard deviation of the population of all such tubes produced by the company?
Given that SAT test scores are normally distributed with a mean of 1000 and a standard deviation of 200, what is the lowest possible score a student needs to qualify for acceptance into the university?
a given projects expected duration along its critical path is 25 days. management wants to know the probability that
To determine whether the mean nicotine content of a brand of cigarettes is greater than the advertised value of 1.4 milligrams, a health advocacy group tests.
1. What is the term used to identify the risk that the client's financial statements may be materially false and misleading?
Researchers conducted an experiment to measure the effect of a drug on improving the quality of sleep as determined by how many more minutes of REM sleep were measured for each participant.
suppose a life insurance company insures the lives of 1000 men aged 30. if actuarial studies show that the probability
Alcohol appears to be involved in a variety of birth defects, including low birth weight and retarded growth. A researcher would like to investigate the effect of prenatal alcohol on birth weight.
Makaela took a spanish exam; her grade was 79. The distribution was normally shaped with xobt =70 and s = 12. Jaun took a history exam; his grade was 86
Is there a significant difference in mean fetal heart rates by position? Run the test at a 5% level of significance.
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