Population Estimation

A research company wants to estimate the proportion of people who like oatmeal.  They want the confidence level to be 95%.  The company gets 325 people to sign up for the survey, but on the day that the survey is issued, only 250 people show up and take the survey.  What happens to the confidence interval?

• It gets larger

• It gets smaller

• It stays the same

• Too little information given

In a survey of 104 students, it was found that 79 went to the homecoming game this year. A 99% confidence interval for p is (0.652, 0.868). Interpret this interval.

• 99% of the time the true proportion of people who went to the homecoming game this year is between 65.2% and 86.6%.

• The probability that the population proportion of people who went to the homecoming game this year is between 65.2% and 86.6% is 95%.

• Based on this sample, I am 99% confident that the true proportion of people who went to the homecoming game this year is between 65.2% and 86.6%.

• 99% of all possible intervals calculated this way will capture the true proportion of people who went to the homecoming game this year

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

A research group wishes to estimate the mean amount of time (in hours) that members of a fitness center spend exercising each week. They want to estimate the mean within a margin of error of 0.5 hours with a 95% level of confidence. Previous data suggests that the standard deviation of the population is 2.2. Which of the following is the smallest sample size they could use?

• 60

• 75

• 90

• 180

A sample of 600 ninth graders was selected at random and asked how much time they spend on homework each day. Of the ninth graders selected, 220 spend less than 2 hours on homework each day. If the conclusion was drawn that “approximately 1.35 million ninth graders spend less than 2 hours on homework each day,” which of the following is closest to the population, in millions, of ninth graders?

• 0.368

• 0.495

• 3.68

• 5.84

A sample of 600 ninth graders was selected at random and asked how much time they spend on homework each day. Of the ninth graders selected, 220 spend less than 2 hours on homework each day. If the conclusion was drawn that “approximately 1.35 million ninth graders spend less than 2 hours on homework each day,” which of the following is closest to the population, in millions, of ninth graders?

• 0.368

• 0.495

• 3.68

• 5.84

A survey conducted on 100 households in a neighborhood finds that the average number of pets per household is 3 with a margin of error of ±0.5. Estimate the mean number of pets in all 500 households in the neighborhood.

• between 1250 pets-1750 pets

• between 125 pets- 175 pets

• between 1820 pets- 1940 pets

• between 182 pets- 194 pets

• between 5,700 and 6,000

• between 6,500 and 7,000

• between 5,400 and 6,600

• between 5,400 and 5,900

If the mean of a sample is 203 and the margin of error is 4.6, what would be a reasonable mean for the population?

• 99.2

• 198.3

• 207.2

• 207.7