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Ch 17 Alternative Hypotheses, P-Values & Using the TI-84 Calculator

Last updated almost 5 years ago

10 questions

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Question 1

1.

Draggable item		Corresponding Item

Question 2

2.

Put the following steps of a hypothesis test in order:

We form an alternative hypothesis that is either one- or two-tailed based on what we want to learn.
We proceed with our test, drawing the hypothesized model and calculating the z-value for the data.
We state our conclusion in the context of the original question.
We form a null hypothesis specifying the parameter of a model we'll test using our data.
We check the appropriate assumptions and conditions.

Question 3

3.

According to national studies, 30% of young adult Americans (ages 18-30) report attending a religious service at least once a week. A group of local clergy men believes the percentage is higher in their area.
State the null and alternative hypothesis:
Ex.

Question 4

4.

According to national studies, 30% of young adult Americans (ages 18-30) report attending a religious service at least once a week. A group of local clergy men believes the percentage is higher in their area so they employ a polling organization.
A poll finds that 48 out of 132 randomly sampled young adults report attending religious services at least once a week. Is this convincing evidence that the proportion is higher in this town?
Use the TI-84 to perform a 1-Proportion Z-Test:
Stat, Calc, #5 (1-PropZTest)
Give the z-score for this sample.

Question 5

5.

Continue the study of young adults attending religious services.
Using the z-score from #4, is this convincing evidence that the proportion is higher in this town?

Yes, there is strong evidence that the proportion of young adults who attend religious services at least once per week is greater than 30% because the sample had a z-score that is more than two standard deviations away from the given proportion.

Yes, there is strong evidence that the proportion of young adults who attend religious services at least once per week is greater than 30% because the sample had a z-score that is not more than two standard deviations away from the given proportion.

No, there is not strong evidence that the proportion of young adults who attend religious services at least once per week is greater than 30% because the sample had a z-score that is more than two standard deviations away from the given proportion.

Question 6

6.

Continue the study of young adults attending religious services.
A poll finds that 48 out of 132 randomly sampled young adults report attending religious services at least once a week. Is this convincing evidence that the proportion is higher in this town?
You performed a 1-Proportion Z-Test in #4, what was the P-Value?

Question 7

7.

What does the P-Value from #6 mean?

There is a 5.5% chance of getting the higher percentage of young adults that attend a religious service at least once per week even if the area's percentage is equal to 30%. This is not very likely and adds weight to the decision to not reject the null hypothesis.

There is a 94.5% chance of getting the higher percentage of young adults that attend a religious service at least once per week even if the area's percentage is equal to 30%. This is very likely nad adds weight to the decision to not reject the null hypothesis

Question 8

8.

Continue the study of young adults attending religious services, the proportion is thought to be 30% for the area.
A poll finds that 48 out of 132 randomly sampled young adults report attending religious services at least once a week. You will determine if the sample proportion is within the 95% confidence interval?

Create a 1-Proportion Z-Interval:
Stat, Test, alpha, math.

Record the interval using parenthesis, separate the values by a comma followed by a space.

Round the values to three places past the decimal point.

Question 9

9.

Continue the study of young adults attending religious services, the proportion is thought to be 30% for the area.
A poll finds that 48 out of 132 randomly sampled young adults report attending religious services at least once a week. Is this convincing evidence that the proportion is higher in this town?
Calculate the sample proportion, is it within the 95% confidence interval you created for #8? (this is another way to check for statistical significance!)
List the sample proportion (rounded to three places past the decimal) followed by a comma and
give your answer of yes or no.
Ex. 0.489, no

Question 10

10.

Match each term with the description

What we should conclude is true if the data are out of line with our original assumption about the parameter.

The value from the population or observed in the past that is claimed not to have changed or to not be different in the null hypothesis.

We calculate a proportion from the sample, then look to see how likely it would be to observe this statistic if the null hypothesis were actually true.

What we should do if it's reasonable to believe that our observed data could have occurred by chance, nothing unusual has happened.

We accept or reject the null hypothesis, give our reason and state this in context of the problem.

We reject the null hypothesis when in fact it is true.  Like a false negative.

We don't reject the null hypothesis when in fact it was false.  Like a false positive.

Used to determine statistical significance. A calculation that tells us how many standard deviations a value is away from the population proportion or mean.

We make a decision: if the data are far out of line with the null hypothesis model, we will reject the null hypothesis that nothing has happened, OR if the data are consistent with the null hypothesis model, we will not reject the hypothesis.

No, there is not strong evidence that the proportion of young adults who attend religious services at least once per week is greater than 30% because the sample had a z-score that is not more than two standard deviations away from the given proportion.