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(a)
To find:
The null and alternative hypotheses for given scenario.
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Answer to Problem 9E
Solution:
The alternate hypothesis is
Explanation of Solution
Given information:
There is an old wives’ tale that women who eat chocolate during pregnancy are more likely to have happy babies. A pregnancy magazine wants to test this claim, and it gathers 100 randomly selected pregnant women for its study. Half of the women sampled agree to cat chocolate at least once a day, while the other half agree to forego chocolate for the duration of their pregnancies. A year later, the ladies complete a survey regarding the overall happiness of their babies. The results are given in the following table. At the 0.01 level of significance, test the claim of the old wives’ tale.
Number of babies | ||
Happy babies | Unhappy Babies | |
With chocolate | 24 | 26 |
Without chocolate | 22 | 28 |
Concept:
The null hypothesis is a statement of no difference, that there is no significant difference between the two phenomena. It is considered to be true until it is nullified by statistical evidence for an alternative hypothesis.
An alternative hypothesis is a contradicting statement to the null hypothesis and states a significant difference between the two phenomena It is accepted when the null hypothesis is false.
Assume, be the estimate proportion for the happy babies whose mothers ate chocolate during their pregnancies.
And be the estimate proportion for the happy babies whose mothers did not eat chocolate during their pregnancies.
From the given information, the claim is made that the pregnant women gives happy child after having chocolates, that is,
The required alternate hypothesis is
It is known that the null hypothesis for the given proportion is
(b)
To find:
The distribution is to be used for the statistical test and its level of significance.
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Answer to Problem 9E
Solution:
The standard normal variate z-test will be applied for given samples at the level of significance is
Explanation of Solution
Given information:
There is an old wives’ tale that women who eat chocolate during pregnancy are more likely to have happy babies. A pregnancy magazine wants to test this claim, and it gathers 100 randomly selected pregnant women for its study. Half of the women sampled agree to cat chocolate at least once a day, while the other half agree to forego chocolate for the duration of their pregnancies. A year later, the ladies complete a survey regarding the overall happiness of their babies. The results are given in the following table. At the 0.01 level of significance, test the claim of the old wives’ tale.
Number of babies | ||
Happy babies | Unhappy Babies | |
With chocolate | 24 | 26 |
Without chocolate | 22 | 28 |
Since the both
According to the null hypothesis, left-tailed test is to be applied.
From the given information, the level of significance is
(c)
To find:
The test statistic for a hypothesis test for two population means.
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Answer to Problem 9E
Solution:
The test statistic value for given population is
Explanation of Solution
Given information:
There is an old wives’ tale that women who eat chocolate during pregnancy are more likely to have happy babies. A pregnancy magazine wants to test this claim, and it gathers 100 randomly selected pregnant women for its study. Half of the women sampled agree to cat chocolate at least once a day, while the other half agree to forego chocolate for the duration of their pregnancies. A year later, the ladies complete a survey regarding the overall happiness of their babies. The results are given in the following table. At the 0.01 level of significance, test the claim of the old wives’ tale.
Number of babies | ||
Happy babies | Unhappy Babies | |
With chocolate | 24 | 26 |
Without chocolate | 22 | 28 |
Formula used:
The formula used to perform a statistic test for a hypothesis test for two population proportions is,
Where,
The weighted estimated proportion for the population is
Also
Calculation:
From the problem, the sample successes are
It is already assumed that
The sample success and size for sample 1 is
Substitute for
in above equation.
The sample success and size for sample 2 is
Substitute
The weighted estimated proportion for the population is given as,
Substitute ,
,
for
and
in above equation.
The statistical test for two population proportions is given as
From equations (1),(2) and (3), substitute for
It is given that the null hypothesis for the given proportion is
Thus, the test statistic value is
(d)
To find:
The value and conclude the decision at given level of significance.
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Answer to Problem 9E
Solution:
The claim is incorrectly made that the pregnant women gives happy child after having chocolates. There will no difference between babies by eating chocolates.
Explanation of Solution
Given information:
There is an old wives’ tale that women who eat chocolate during pregnancy are more likely to have happy babies. A pregnancy magazine wants to test this claim, and it gathers 100 randomly selected pregnant women for its study. Half of the women sampled agree to cat chocolate at least once a day, while the other half agree to forego chocolate for the duration of their pregnancies. A year later, the ladies complete a survey regarding the overall happiness of their babies. The results are given in the following table. At the 0.01 level of significance, test the claim of the old wives’ tale.
Number of babies | ||
Happy babies | Unhappy Babies | |
With chocolate | 24 | 26 |
Without chocolate | 22 | 28 |
Formula Used:
The
When
It is already computed that
And the level of significance is
The null hypothesis is accepted as
Thus, the claim is incorrectly made that the pregnant women gives happy child after having chocolates. There will no difference between babies by eating chocolates.
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Chapter 11 Solutions
Beginning Statistics, 2nd Edition
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