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
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