3/3/2023

Hypothesis Testing for One Proportion

• Setting and notation
• See cellphone.R - A 2012 survey of 2,254 American adults indicates that 384 or approximately 17% of cell phone owners do their browsing on their phone rather than a computer or other device. Find a 95% confidence interval for the true proportion of American adults who use their phones to browse the web. Is the true proportion significantly less than 20%?
• Follow up: Fast forward to 2023 - how many of us use our cell phones to browse the web? Answer: _8_ out of _13_, so we can use binom.test() to find a confidence interval or do a test.

Class Exercises

Home Field Advantage 

Is there really a home-field advantage in baseball? In the 1991 National League season, the home team won 532 games and lost 438 games. Conduct an appropriate hypothesis test using significance level 0.05.

Penny Spinning

Suppose that a student spins a coin 100 times and gets 38 heads. Do we have statistically significant evidence that the chance of getting a head is less than 50%? Use a 0.01 level test.

Preference study 

The American Orthopedic Foot and Ankle Society (1998) conducted a telephone interview of 531 women who worked outside the home. They reported that 234 of the women wore “flats” to work. Do the data provide evidence to refute the claim that p=.4? Use a significance level of 0.05.

Sample Size Determination

You wish to use a random sample of size n to construct an approximate C.I. for p that will have margin of error no greater than .05. How large should n be if you want your approximate confidence in the interval to be 95%?

Please read Section 6.1 for class on Monday after Spring Break. Have a fantastic break!