Proportion Confidence Intervals and Hypothesis Testing

• 0.90

• 0.40

• 0.05

• 0.20

• 0.10

A claimed psychic was presented with 200 cards face down and asked to determine if the card was one of five symbols: a star, cross, circle, square, or three wavy lines.  The "psychic" was correct in 50 cases.  To determine if he has ESP, we test the hypothesis H₀:  p = 0.20, Hₐ: p > 0.20, where p represents the true proportion of cards for which the psychic would correctly identify the symbol in the long run.  Assume the conditions for inference are met.  The P-value is 

• between .10 and .05

• between .05 and .025

• between .025 and .01

• between .01 and .001

An SRS of 100 teachers showed that 64 owned smartphones.  An SRS of 100 students showed that 80 owned smartphones.  Let pₑ be the proportion of all teachers who own smartphones, and let pₓ be the proportion of all students who own smartphones.  A 95% confidence interval for the difference pₑ - pₓ is 

• (0.264, 0.056)

• (0.098, 0.222)

• (-0.222, -0.098)

• (-0.283, -0.038)

A simple random sample of 1000 Americans found that 62% were satisfied with the service provided by the dealer from which they bought their car.  A simple random sample of 1000 Canadians found that 59% were satisfied with the service provided by the dealer from which they bought their car.  The sampling variability associated with these statistics is

• exactly the same

• not exactly the same, but very close

• much smaller for the sample of Canadians because the population of Canad is much smaller than that of the United States, hence the sample is a larger proportion of the population.

• smaller for the sample of Canadians because the percent satisfied was smaller than that of Americans.

A recent study of 750 Internet users in Europe found that 35% of Internet users were women.  What is the 95% confidence interval of the true proportion of women in Europe who use the Internet? 

• 0.321 < p < 0.379

• 0.316 < p < 0.384

• 0.309 < p < 0.391

• 0.305 < p < 0.395

A survey of 800 women shoppers found that 17% of them shop on impulse.  What is the 98% confidence interval for the true proportion of women shoppers who shop on impulse? 

• 0.148 < p < 0.192

• 0.136 < p < 0.204

• 0.144 < p < 0.196

• 0.139 < p < 0.201

It was found that in a sample of 90 teenage boys, 70% of them have received speeding tickets.  What is the 90% confidence interval of the true proportion of teenage boys who have received speeding tickets? 

• (0.621, 0.780)

• (0.591, 0.812)

• (0.584, 0.830)

• (0.615, 0.805)

Which of the following actions would produce a confidence interval with a smaller width assuming all other contingencies remained constant?

• Using a higher confidence level

• Using a lower confidence level

A random sample of 425 citizens of Naboo found that 34% support the Galactic Republic. A sample of 585 citizens of Tatooine found that 38% support the Galactic Republic. What test would you use to determine if the the proportions are different?

• 2 sample z-test for mean 

• 2 sample t-test for mean

• matched-pairs dependent sample t-test for mean

• 2 - proportion z test

A Keebler sales rep claims that there are more chocolate chips in their cookie than in Chips Ahoy cookies.  You take a random sample of 20 Keebler cookies and find an average of 15.8 chips per cookie and a s = 3.7 chips. A random sample of 25 Chips Ahoy yields 14.2 chips per cookie and s = 4.3 chips. What is the conclusion of the test?

• There is enough evidence to reject the claim that there are more chips in Keeblers.

• There is not enough evidence to reject the claim that there are more chips in Keeblers.

• There is enough evidence to support the claim that there are more chips in Keeblers.

• There is not enough evidence to support the claim that there are more chips in Keeblers.