# Null hypothesis and alternative hypothesis examples

1. Identify the null hypothesis and the alternative hypothesis. A researcher claims that 62% of voters favor gun control.

H0: p < 0.62

H1:p >= 0.62

H0: p = 0.62

H1: p not = 0.62

H0: p not = 0.62

H1: p = 0.62

H0: p > = 0.62

H1: p < 0.62

2. Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis given alpha= 0.05 for a left-tailed test.

3. Use the given information to find the P-value. The test statistic in a right-tailed test is z = 1.43

4. Find the P-value for the indicated hypothesis test.

In a sample of 124 children selected randomly from one town, it is found that 38 of them suffer from asthma. Find the P-value for a test of the claim that the proportion of all children in the town suffer from asthma is equal to 28%.

5. Assume that a simple random sample has been selected from a normally distributed population. Calculate the test statistic (include it in your answer: z, t, x^2, F...).

A researcher is testing the claim that the mean age of the prison population in one city is less than 26 years. Sample data are summarized as n = 25, x-bar = 24.4 years, and s = 9.2 years. The significance level is alpha = 0.05

6. Decide (circle) which sampling distribution applies to the following information.

Claim: population mean, u = 111. Sample data: n = 10, x-bar = 101, s = 15.3. The sample data appear to come from a normally distributed population with unknown mean and unknown standard deviation.

Normal Student t Chi-Square None of the above.

7. Formulate the indicated conclusion. Be sure to address the original claim.

A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the population standard deviation, sigma = 3.3 mg, stated by the manufacturer. Assuming that a hypothesis test of the researcher's claim has been conducted and that the decision is "fail to reject the null hypothesis", state the conclusion.

8. Calculate the test statistic (include it in your answer: z, t, x^2, F...).

The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25, and the sample statistics include n = 650 drowning deaths of children with 30% of them attributable to beaches.

9. Assume that a hypothesis test of the given claim will be conducted. Identify the type I error for the test .

The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a mean temperature, u= 46 degrees farenheit, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims that the stated mean temperature is incorrect.

A. Failing to reject the hypothesis that the mean temperature equals 46 degree fahrenheit when it is really different from 46 degree fahrenheit

B. Rejecting the hypothesis that the mean temperature equals 46 degree fahrenheit when it really is different from 46 degree fahrenheit.

C. Rejecting the hypothesis that the mean temperature equals 46 degree fahrenheit when it really does equal 46 degree fahrenheit.

D. Failing to reject the hypothesis that the mean temperature is less than 46 degree fahrenheit when it really is more than 46 degree fahrenheit.

10. Find the critical value of Chi-Square based on the given information.

The alternative hypothesis is sigma is less than 0.68, the sample size is n = 19, and alpha= 0.025

11. From the sample statistics, find the value of the pooled proportion p-bar used to test the hypothesis that the population proportions are equal.

n1 = 48 x1 = 7 n2 = 455 x2 = 260

12. Calculate the test statistic (include it in your answer: z, t, x^2, F...) used to test the null hypothesis that p1 = p2

A report on the nightly news broadcast stated that 12 out of 150 households with pet dogs were burglarized and 28 out of 224 households without pet dogs were burglarized.

13. Based on #12: Is the reported justified in stating that households with dogs are less likely to be burglarized? Why?

14. Find the critical values for a two-tailed hypothesis test of the standard deviation based on the following values: n1 = 9, n2 = 7,alpha = 0.05

15. Decide whether this represents independent samples or matched pairs.

The effectiveness of a headache medicine is tested by measuring the intensity of a headache in patients before and after drug treatment. The data consist of before and after intensities for each patient.

16. Decide whether this represents independent samples or matched pairs.

The effect of caffeine as an ingredient is tested with a sample of regular soda and another sample with decaffeinated soda.

17. A farmer has decided to use a new additive to grow his crops. He divided his farm into 10 plots and kept records of the corn yield (in bushels) before and after using the additive. The results are shown below.

Plot 1 2 3 4 5 6 7 8 9 10

Before 9 7 8 9 6 8 6 10 10 7

After 10 8 10 11 6 10 8 11 11 9

Test the following hypothesis at the 5% level of significance.

H0: ud = 0

H1: ud ≠ 0

What is the appropriate test statistic? (include it in your answer: z, t, x^2, F...)

What is the critical value? (include it in your answer: z, t, x^2, F...)

What is the decision?

Write a few sentences for your conclusion

https://brainmass.com/statistics/hypothesis-testing/null-hypothesis-and-alternative-hypothesis-examples-105664

#### Solution Summary

Testing of hypothesis using STATDISK.

Hypothesis Testing: Null and Alternate Hypotheses, P Value

Four Hypothesis Testing problems

Problem 10.17: M&M/Mars claims that at least 20% of the M&M's in each package are the new blue color. Set up the null and alternate hypotheses to test this claim.

Problem 10.18: The computer center at a university claims that the average amount of time that students spend on-line has increased from last year's average of 1 hour per day. Set up the null and alternative hypotheses to test this claim.

Problem 10.20: Recent medical research indicates that skin cancer patients who receive a new medication for skin cancer live longer than those who do not. The average length of life prior to the development of this medication was 18 months. The medical community wishes to test the claim made by the developers of this drug. A sample of 35 patients who received the medication lived an average of 21 months. The standard deviation is 5 months.

a) Set up the null and the alternative hypotheses to test if average length of life has increased from 18 months.

b) Test your hypotheses using a = 0.05.

c) Find the p value.

d) Based on the p value, what can you conclude about the average length of life for patients who receive the vaccine?

Problem 10.22: A manufacturer of top-of-line tennis rackets claims that its Smack Em tennis racket will change a player's game. A tennis pro currently serves the ball at an average speed of 115 mph with a standard deviation of 2.5 mph. The speeds are normally distributed. The tennis pro decides to test the company's claim and records the speed of his serve for 15 balls using the Smack Em racket. The data are shown in the following table: Speed

117.3 115.9

115.1 115.2

116.0 115.0

116.2 113.0

112.9 120.8

115.4 116.9

113.8 114.4

114.2

a) Set up the null and the alternative hypotheses to test if the average service speed has increased using the new racket.

b) Test your hypotheses using a = 0.05

c) Find the p value.

d) Based on the p value, should the tennis pro invest in the new racket?