# Hypothesis Testing of Mean & Proportion

You will be asked to determine the correct decision (Reject Ho or Fail to Reject Ho) for each of the following tests of hypotheses.

1. A hypothesis test at the 0.05 level of significance with a p-value for the sample of 0.105.

2. A hypothesis test at the 0.025 level of significance with a p-value for the sample of 0.002.

3. A two-tailed hypothesis test at the 0.05 level of significance where the initial probability calculated for the test statistic is 0.035. (Don't forget to make the adjustment needed for the two tailed test.)

4. A two-tailed hypothesis test with critical values of ±2.33 and a test statistic for the sample of -2.56.

5. A one tailed hypothesis test with a critical value of 2.306 and a test statistic for the sample of 1.652.

6. A one tailed hypothesis test with a critical value of -1.796 and a test statistic for the sample of -.843.

You will be asked to determine the correct prob-value in each of the following situations. You may assume data sets are normally distributed.

7. A right-tailed test with z = 1.57 based on a sample larger than 50. You may assume the data is normally distributed.

8. A two-tailed test with t = -2.552 based on a sample of size 20. You may assume the data is normally distributed. (To match my answer you will need to use Minitab to get this value.)

You will be asked to determine the correct critical value(s) in each of the following situations. You may assume data sets are normally distributed.

9. A two-tailed test with alpha = 0.025. You may assume the value of std deviation is known.

10. A left-tailed test with alpha = 0.10, unknown std deviation, and a sample of size 35. You may assume the data is normally distributed.

1. A medical school claims that more than 28% of its students plan to go into general practice.

a. It is found that among a random sample of 130 of the school's students, 42 of them plan to go into general practice. Does this sample evidence support the school's claim? Use the p-value approach and alpha = 0.05 to make your decision.

b. Suppose a second sample is collected a year after the first with the results indicating 57 out of 135 plan to go into general practice. Does this sample evidence support the school's claim? Use the p-value approach and alpha= 0.05 to make your decision.

2. The health of employees is monitored by periodically weighing them. A sample of 54 employees has a mean weight of 183.9 lbs. Assuming that std deviation is known to be 121.2 lb. Use a 0.10 level to test the claim that the population mean weight of all such employees is less than 200 lb.

3. A manufacturer makes ball bearings that are supposed to have a mean weight of 30 g. A retailer suspects that the mean weight is not 30 g and wants to verify that the product is meeting specifications. The mean weight for a random sample of 16 ball bearings is 29.5 g with a standard deviation of 4.1 g. At the 0.05 significance level, test the claim that the mean is not 30 g. You may assume the weights are normally distributed.

4. In tests of a computer component, it is found that the mean time between failures is 520 hours. A modification is made which is supposed to increase the time between failures. Tests on a random sample of 10 modified components resulted in the following times (in hours) between failures.

518 548 561 523 536

499 538 557 528 563

a. Find x-bar and s for this data set.

b. At the 5% significance level, test the claim that for the modified components, the mean time between failures is greater than 520 hours? You may assume the times between failures are normally distributed. Use the traditional method to make your decision.

5. A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. The weights (in ounces) of the cereal in a random sample of 8 of its cereal packets are listed below.

14.6 13.8 14.1 13.7 14.0 14.4 13.6 14.2

At the 0.01 significance level, does the sample support the company's claim that the mean weight is at least 14 ounces? You may assume the weight of cereal packets is normally distributed.

6. Various temperature measurements are recorded at different times for a particular city. The mean of 21°C is obtained for 32 temperatures on 32 different days. Assuming that ? = 1.5°C, test the claim that the population mean is actually less than 22°C. Use a 0.05 significance level.

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#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

Hypothesis testing: z test for soda filled bottles; z test for new medical claims system

See attached two files.

In first file there are 2 questions. MOST IMPORTANT is these problems need be done using the second utility file.

The following data represent the actual amount of soda in a sample of fifty 2-liter bottles. You are in charge of production and must assure that the bottles don't have too much or too little in them. At the 0.05 level of significance, is there evidence to suggest that the mean amount of soda filled is different from 2.0 liters?

Q-1a: State the null hypothesis.

Q-1b: State the alternate hypothesis.

Q-1c: Perform the hypothesis test and state your conclusions and evidence.

Suppose you didn't care if the bottles had too much, you only cared if the quantity in the bottles was less than 2.0 liters.

Q-1d: State the new null hypothesis.

Q-1e: State the new alternative hypothesis.

Q-1f: Perform the hypothesis test and state your conclusions and evidence.

Late payment of medical claims can add to the cost of health care. The auditing firm of Dewey, Cheatham, and Howe has discovered that for one insurance company, 85.1% of the claims were paid in full when first submitted based on a sample of 200 claims. Suppose that the insurance company developed a new payment system in an effort to increase this percentage. A sample of 200 claims processed under this new system revealed that 180 of the claims were paid in full when first submitted. At the 5% level of significance, is there evidence that the population proportion of claims paid in full under this new system is higher than the proportion of claims paid in full under the old system?

Q-2a: State the null hypothesis

Q-2b: State the alternative hypothesis.

Q-2c: Perform the hypothesis test and state your conclusions and evidence.

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