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ILLOWSKYINTROSTAT1 9.5.080.HW.

MY NOTES

ASK YOUR TEACHER

PRACTICE ANOTHER
Your statistics instructor claims that 60 percent of the students who take her Elementary Statistics class go through life feeling more enriched. For some reason that she can't quite figure out, most people don't believe her. You decide to check this out on your own. You randomly survey 64 of her past Elementary Statistics students and find that 34 feel more enriched as a result of her class. Now, what do you think? Conduct a hypothesis test at the 5% level.

Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Part (a)
Part (b)
Part (c)
Part (d)
State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom.)

Part (e)
What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)

Correct: Your answer is correct.
=
Part (f)
What is the p-value? (Round your answer to four decimal places.)


Explain what the p-value means for this problem.
If H0 is false, then there is a chance equal to the p-value that the sample ratio is not 34 out of 64 or more.
If H0 is false, then there is a chance equal to the p-value that the sample ratio is 34 out of 64 or less.
If H0 is true, then there is a chance equal to the p-value that the sample ratio is not 34 out of 64 or more.
If H0 is true, then there is a chance equal to the p-value that the sample ratio is 34 out of 64 or less.
Correct: Your answer is correct.
Correct! A p-value is the probability that an outcome of the data will happen purely by chance when
H0
is true.
Part (g)

Part (h)
Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
=

(ii) Decision:
reject the null hypothesis
do not reject the null hypothesis
Correct: Your answer is correct.

(iii) Reason for decision:
Since < p-value, we do not reject the null hypothesis.
Since > p-value, we do not reject the null hypothesis.
Since < p-value, we reject the null hypothesis.
Since > p-value, we reject the null hypothesis.
Correct: Your answer is correct.

(iv) Conclusion:
There is sufficient evidence to conclude that less than 60% percent of her students feel more enriched.
There is not sufficient evidence to conclude that less than 60% percent of her students feel more enriched.
Correct: Your answer is correct.
Part (i)
Construct a 95% confidence interval for the true proportion. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your answers to four decimal places.)
WebAssign Plot
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