A new cold medication claims that, on average, individuals who take the medication recover within 5 days. Dr. Nelson believes the recovery time is longer. She surveys 31 people with colds who take the medication. She finds that their recovery time, in days, is as follows: 7, 5, 4, 8, 5, 5, 4, 4, 5, 5, 6, 4, 4, 5, 4, 7, 5, 7, 4, 6, 4, 3, 5, 7, 8, 4, 7, 4, 6, 4, 6 Perform a hypothesis test using a 9% level of significance. Step 1: State the null and alternative hypotheses. Ho: pV (So we will be performing a right-tailed test.) Step 2: Assuming the null hypothesis is true, determine the features of the distribution of point estimates using the Central Limit Theorem. By the Central Limit Theorem, we know that the point estimates are t-distributed with distribution mean and distribution standard deviation Step 3: Find the p-value of the point estimate. P(& v ) = P(tv 2v p-value = %3D Step 4: Make a Conclusion About the null hypothesis. Since the p-value = = a, we do not reject the null %3D hypothesis. We cannot reject the claim that, on average, individuals who take the medication recover

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A new cold medication claims that, on average, individuals who take the medication recover within 5
days. Dr. Nelson believes the recovery time is longer. She surveys 31 people with colds who take the
medication. She finds that their recovery time, in days, is as follows:
7, 5, 4, 8, 5, 5, 4, 4, 5, 5, 6, 4, 4, 5, 4, 7, 5, 7, 4, 6, 4, 3, 5, 7, 8, 4, 7, 4, 6, 4, 6
Perform a hypothesis test using a 9% level of significance.
Step 1: State the null and alternative hypotheses.
H.: pv >v
(So we will be performing a right-tailed
Vv test.)
Step 2: Assuming the null hypothesis is true, determine the features of the distribution of
point estimates using the Central Limit Theorem.
By the Central Limit Theorem, we know that the point estimates are t-distributed
v with
distribution mean
and distribution standard deviation
Step 3: Find the p-value of the point estimate.
P( 2v
= P(tv 2v
%3D
p-value =
Step 4: Make a Conclusion About the null hypothesis.
Since the p-value =
= a, we do not reject
the null
hypothesis.
O We cannot reject the claim that, on average, individuals who take the medication recover
within 5 cdays
Transcribed Image Text:A new cold medication claims that, on average, individuals who take the medication recover within 5 days. Dr. Nelson believes the recovery time is longer. She surveys 31 people with colds who take the medication. She finds that their recovery time, in days, is as follows: 7, 5, 4, 8, 5, 5, 4, 4, 5, 5, 6, 4, 4, 5, 4, 7, 5, 7, 4, 6, 4, 3, 5, 7, 8, 4, 7, 4, 6, 4, 6 Perform a hypothesis test using a 9% level of significance. Step 1: State the null and alternative hypotheses. H.: pv >v (So we will be performing a right-tailed Vv test.) Step 2: Assuming the null hypothesis is true, determine the features of the distribution of point estimates using the Central Limit Theorem. By the Central Limit Theorem, we know that the point estimates are t-distributed v with distribution mean and distribution standard deviation Step 3: Find the p-value of the point estimate. P( 2v = P(tv 2v %3D p-value = Step 4: Make a Conclusion About the null hypothesis. Since the p-value = = a, we do not reject the null hypothesis. O We cannot reject the claim that, on average, individuals who take the medication recover within 5 cdays
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