Assume that the data has a normal distribution and the number of observation is greater than fifty.  Find the critical z value used to test a null hypothesis.  a = 0.09 for a right tailed test.

Compute the test statistic. Find the​ P-value. State the conclusion.

Identify Ho and Ha for a paired t-test to determine if there is a difference in the number of breeding horseshoe crabs from 2011 to 2012:  The mean difference between paired observations is zero.  The mean difference between paired observations is not zero. Use the paired t-test function (=ttest(array1, array2, tails, type) to determine the if the two sets of measurements are correlated with each other. Report your answer to three decimal places.  Do you fail to reject or reject the null hypothesis?  Were the number of breeding horseshoe crabs the same or different between between the two years?

A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 45 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 46.4 milligrams. Assume the population is normally distributed and the population standard deviation is 6.2 milligrams. At a = 0.05, can you reject the company's claim? Complete parts (a) through (e). (a) Identify Ho and Ha. Choose the correct answer below. A. Ho: µ# 45 Hai µ= 45 B. Ho: µ+ 46.4 Hai H= 46.4 %3D O c. H: μ= 46.4 Ha: µ# 46.4 D. Ho: μ246.4 Hai H<46.4 %3D E. Ho: µ= 45 Hai µ#45 ΟF H0 : μ2 45 Ha: p<45 (b) Find the critical value(s). Select the correct choice below and fill in the answer box within your choice. (Round to two decimal places as needed.) O A. The critical value is O B. The critical values are +

Medical Operations The director of a medical hospital feels that her surgeons perform more operations per year than the national average of 211. She selected a random sample of 15 surgeons and found that the mean number of operations they performed was 212.8. The standard deviation of the sample was 3.8. Is there enough evidence to support the director's feelings at a = 0.10? Assume that the population is approximately normally distributed. Use the critical value method and tables. compute the test- using the the z- test find the p value make a decision

A machine at a food-distribution factory fills boxes of rice. The distribution of the weights of filled boxes of rice has an approximately Normal distribution, with a mean of 28.2 ounces and a standard deviation of 0.4 ounces. Boxes are often weighed before shipping, and any box with a weight of at most 27.5 ounces is considered underweight and is rejected for distribution. What percentage of filled boxes of rice are rejected for distribution? Find the z-table here.

Previous research has shown that the mean number of ballpoint pens Americans use per year is 4.3 with a standard deviation of 1.17. You believe that amount is too high since computers are used so often this day and age. You randomly select 20 people and find the average to be 3.8 ballpoint pens per year. Assuming normality, is there evidence to show that the mean has decreased? What is the decision for this hypothesis test? Previous research has shown that the mean number of ballpoint pens Americans use per year is 4.3 with a standard deviation of 1.17. You believe that amount is too high since computers are used so often this day and age. You randomly select 20 people and find the average to be 3.8 ballpoint pens per year. Assuming normality, is there evidence to show that the mean has decreased? What is the decision for this hypothesis test?  Reject the null because the test statistic is in the critical region and the p-value is less than alpha.  Reject the null because the test…

Let x be a random variable representing the SAT math score of student. We may assume that x has a normal distribution and that the population standard deviation is 25. A large university claims the average SAT math score for incoming freshman is 650. You suspect that this claim is too high and decide to test the claim. You select a random sample of 75 incoming freshman and find the sample mean SAT math score to be 645. If you assume that the population mean is 650, find the P-value corresponding to the hypothesis that the average SAT score is less than 650 (i.e. left-tail test).   A. 0.037   B. 0.061   C. 0.042   D. 0.053

A medical researcher wants to investigate the amount of time it takes for patients' headache pain to be relieved after taking a new prescription painkiller. She plans to use statistical methods to estimate the mean of the population of relief times. She believes that the population is normally distributed with a standard deviation of 15 minutes. How large a sample should she take to estimate the mean time to within 3 minutes with 93% confidence? ... Sample Size = Note:

A researcher believes that the mean age of medical doctors in a large hospital system is older than the average age of doctors in the United States, which is 46. Assume the population standard deviation is 4.2 years. A random sample of 30 doctors from the system is selected, and the mean age of the sample is 48.6. Test the claim at a = 0.05.