A random sample of 100 observations from a population with standard deviation 71 yielded a sample mean of 112. Complete parts a through c below. a. Test the null hypothesis that μ = 100 against the alternative hypothesis that μ> 100, using a = 0.05. Interpret the results of the test. What is the value of the test statistic? Z= (Round to two decimal places as needed.)

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A random sample of 100 observations from a population with standard deviation 39 yielded a sample mean of 107. Complete parts a throughc below. a. Test the null hypothesis that u = 100 against the alternative hypothesis that u > 100, using a =0.05. Interpret the results of the test. What is the value of the test statistic? (Round to two decimal places as needed.) z=

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=74.5σ=74.5. You would like to be 98% confident that your estimate is within 2.5 of the true population mean. How large of a sample size is required?n =

A recent personalized information sheet from your wireless phone carrier claims that the mean duration of all your phone calls was μ=3.1 minutes with a standard deviation of σ=2.4 minutes. From a random sample of n=50 calls, your parents computed a sample mean of x=4.1 minutes and a sample standard deviation of s=3.2 minutes. Complete parts a through e below. a. Sketch the population distribution for the duration of your phone calls. What are its mean and standard​ deviation? b. What are the mean and standard deviation of the data​ distribution? c. Find the mean and standard deviation of the sampling distribution of the sample mean.   d. Is the sample mean of 4.1 minutes unusually​ high? Find its​ z-score and comment.   e. Your parents told you that they will kick you off the plan when they find a sample mean larger than 4.2 minutes. How likely is this to​ happen? ​P(x>4.2 minutes)= ?

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=21.8σ=21.8. You would like to be 98% confident that your estimate is within 0.8 of the true population mean. How large of a sample size is required?n = Do not round mid-calculation.

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=46.9σ=46.9. You would like to be 95% confident that your estimate is within 2 of the true population mean. How large of a sample size is required?n =

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=24.5. You would like to be 90% confident that your estimate is within 2.5 of the true population mean. How large of a sample size is required? Do not round mid-calculation. n =

A B. The mean blood cholesterol level for all men aged 20 to 34 years is p = 188 mg/dl with a standard devlation of a = 41 mg/dl. We suspect that the mean for cross-country runners is lower. A random sample of 20 cross-country runners yielded a mean level of 172 mg/di. SHOW YOUR FORMULAS AND ALL WORK ON THIS PAGE What is the standard deviation of the mean length X? Standard Deviation 41.0000

The human population has a mean IQ score of u = 100 and a standard deviation of o = 15. Find the z- score of a stat student who has an IQ score of 123. Round to 3 decimal places. 1.533 1.118 None of these -1.339 1.779