When should you find the Confidence Interval,

and when should you use a Hypothesis Test?

Page 174

A May 2000 Gallup Poll found that 38% of a random sample of 1012 adults said that they believe in ghosts. Find a 95% confidence interval for the true proportion of adults who believe in ghost.

A May 2000 Gallup Poll found that 38% of a random sample of 1012 adults said that they believe in ghosts. Find a 95% confidence interval for the true proportion of adults who believe in ghost.

Find the confidence interval only.

No hypothesis test is required.

Assumptions:

•Have an SRS of adults

•np =1012(.38) = 384.56 & n(1-p) = 1012(.62) = 627.44 Since both greater than 10, can approximate to normal.

•Population of adults is at least 10,120.

Conclusion: We are 95% confident that the true proportion of adults who believe in ghosts is between 35% and 41%.

AP Format Given: n = 1012p = .38q = .62Phat=.38x = (1012)(.38) = 385

Calculations:

A new flu vaccine claims to prevent a certain type of flu in 70% of the people who are vaccinated. In a test, vaccinated people were exposed to the flu. The test statistic for the results is z = -1.38. Is this claim too high?

A new flu vaccine claims to prevent a certain type of flu in 70% of the people who are vaccinated. In a test, vaccinated people were exposed to the flu. The test statistic for the results is z = -1.38. Is this claim too high?

Use a hypothesis test.

A new flu vaccine claims to prevent a certain type of flu in 70% of the people who are vaccinated. In a test, vaccinated people were exposed to the flu. The test statistic for the results is z = -1.38. Is this claim too high? Write the hypotheses, calculate the p-value & write the appropriate conclusion for = 0.05.

H0: p = .7Ha: p < .7Where p is the true proportion of vaccinated people who get the flu

P-value = normalcdf(-10^99,-1.38) =.0838

Since the p-value > , I fail to reject H0. There is not sufficient evidence to suggest that the proportion of vaccinated people who do not get the flu is less than 70%.

Formula for hypothesis test:Formula for hypothesis test:

statistic of SD

parameter - statisticstatisticTest

z pp ˆ

npp

pp

1

ˆ

P. 174 #2 A magazine is considering the launch of an online edition. The magazine plans to go ahead only if it’s convinced that more than 25% of current readers would subscribe. The magazine contacts a random sample of 500 current subscribers and 137 of those surveyed expressed an interest. Is this sufficient evidence for the magazine to start the online edition?

P. 174 #2 A magazine is considering the launch of an online edition. The magazine plans to go ahead only if it’s convinced that more than 25% of current readers would subscribe. The magazine contacts a random sample of 500 current subscribers and 137 of those surveyed expressed an interest. Is this sufficient evidence for the magazine to start the online edition?

Use a hypothesis test.

Assumptions:

•Have an SRS of current subscribers

•np = 500(.25) = 125 & n(q) = 500(.75) = 375 Since both greater than 10, can approximate to normal.

•Population of subscribers is at least 5000.

Conclusion: Since the p-value is greater than α, I fail to reject the null hypothesis. There is not sufficient evidence for the magazine to start the online edition.

P. 174 #2 AP Format Given: n = 500, x = 137p = .25q = .75phat=137/500 = .274

Calculations:

P-value = normalcdf(1.239,10^99) =.108

Hypotheses: H0: p = .25 α = .05Ha: p > .25Where p is the true proportion of current readers who would subscribe.

REVIEW: Facts about p-values:

• ALWAYS make decision about the null hypothesis!

• Large p-values show support for the null hypothesis, but never that it is true! “Fail to reject”

• Small p-values show support that the null is not true. “Reject”

• Double the p-value for two-tail (=) tests

• Never acceptNever accept the null hypothesis!

At an level of .05, would you reject or fail to reject H0 for the given p-values?

a) .03

b) .15

c) .45

d) .023

Reject

Fail to reject

Fail to reject

Reject

Homework:

• Page 174: Determine which problems should use a Hypothesis Test, and rework those problems.

• Unit 10 Review #1-14 (Finish it)

• Quiz tomorrow