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# Null hypothesis and Alternative hypothesis examples

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1. Although opinion polls have long found that about 40% of American adults say they attend religious services last week, this is almost certainly not true.
a. Why might we expect answers to a poll to overstate true church attendance?
b. You suspect strongly that the true percentage attending church in any given week is less than 40%. You plan to watch a random sample of adults and see whether or not they go to church. What are your null and alternative hypotheses?

2. The national unemployment rate in a recent month was 5.4%. You think the rate may be different in your city, so you plan to ask a sample of the city residents about their employment status. To see if the local rate differs significantly from 5.4% what hypothesis will you test?

3. A social scientist is studying the ages of executives in top management positions and thinks that the mean ages of technology executives is lower than that in other business sectors. What data need to be collected? What hypotheses are needed?

4. What null and alternative hypothesis should we use if we want to test the claim that on average children attending elementary schools in a certain metropolitan area are more than two miles from the school which they attend.

5. The manufacturer of a spot remover claims that his product removes 90 percent of all spots. In a random sample, the spot remover removes 11 of 16 stains. Write the null and alternative hypotheses.

6. In a study of the relationship between family size and intelligence, 49 "only children" had an IQ of 101.5 with a standard deviation of 6.7 and 50 "first born children" in two-child families had a mean IQ of 105.9 with a standard deviation of 5.8. Write out the relevant null and alternative hypothesis.

https://brainmass.com/statistics/hypothesis-testing/null-hypothesis-and-alternative-hypothesis-examples-95006

#### Solution Preview

1. Although opinion polls have long found that about 40% of American adults say they attend religious services last week, this is almost certainly not true.
a. Why might we expect answers to a poll to overstate true church attendance?

Ans.

Respondents' answers in interviewer-assisted modes tend to be biased toward socially acceptable answers. This may be a reason for this error. Postal mail survey, Web surveys are not interviewer-assisted and therefore, are well suited in for this type of research.

b. You suspect strongly that the true percentage attending church in any given week is less than 40%. You plan to watch a random sample of adults and see whether or not they go to church. What are your null and alternative hypotheses?

Ans.

H0: Percentage of adults attending religious service is equal to 40%

#### Solution Summary

Null hypothesis and Alternative hypothesis examples.

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## Testing of hypothesis using STATDISK

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 &#8800; 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

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