Estimating a Population Proportion

A random sample of 100 PHS students found that 53 of them were in possession of a pencil. What is the p-hat for this sample?

• 0.53

• 0.5

• 0.47

• 1

A website asks visitors to vote for which of several user-submitted videos is funniest. After a few days, they have collected 250 votes, and they would like to construct a 95% confidence interval for the true proportion of visitors who prefer one of the videos. However, they recognize that their sampling method involves voluntary response, so the data may be biased. How can they compensate for this problem when constructing their confidence interval?

• Use a lower confidence level, such as 80%.

• Use a higher confidence level, such as 99%.

• Collect an additional 250 votes using an SRS.

• Select a smaller sample.

• Throw this data out. There is no way to compensate for this bias.

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 sample of 400 racing cars showed that 80 cars cost over $700,000. What is the 99% confidence interval of the true proportion of cars costing over $700,000?

• 0.001 < p < 0.005

• 0.566 < p < 0.693

• 0.148 < p < 0.252

• 0.023 < p < 0.045

If 827 represents "no" voters out of 2584, construct a 95% confidence interval for the "no" group.

• [.300,.340]

• [.298,.342]

• [.302,.338]

• [.288,.352]

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 random sample of Houston residents were surveyed about whether they supported raising the fine on speeding tickets. From the results a 95% confidence interval was created to estimate the proportion of people in Houston who support the raising the fine on speeding tickets. The interval was (0.45, 0.59) Based on the confidence interval, which of the following claims is supported?

• More than 90 percent of the residents support the increase.

• More than 60 percent of the residents support the increase.

• More than 40 percent of the residents support the increase.

• Fewer than 25 percent of the residents support the increase.

A mayor is concerned about the percentage of city residents who express disapproval of his job performance.  His political committee pays for a newspaper ad, hoping to keep his disapproval rating below 21%.  They will use a follow up poll to access effectiveness.  What are the correct null and alternative hypotheses?

• Ho: p=.21
  Ha: p > .21

• Ho: p< .21
  Ha: p= .21

• Ho: p> .21
  Ha: p= .21

• Ho: p= .21
  Ha: p< .21

5% of trucks of a certain model have needed new engines after being driven between 0 and 100 miles.  The manufacturer hopes that the redesign of one of the engine's components has solved this problem.  Write the null and alternative hypotheses for this situation.

• Ho:  p< 0.05
  Ha:  p = 0.05

• Ho:  p = 0.05
  Ha:  p > 0.05

• Ho:  p = 0.05
  Ha:  p < 0.05

• Ho:  p > 0.05
  Ha:  p = 0.05

A company hopes to improve its engines, setting a goal of no more than 3% of customers using their warranty on defective engine parts.  A random survey of 1200 customers found only 20 with complaints.  Create a 95% confidence interval for the true level of warranty users among all customers.

• Based on the data we are 95% confident the proportion of warranty users is between 0.9% and 2.4%.  Therefore the company met its goal.

• Based on the data we are 95% confident the proportion of warranty users is between 2.0% and 2.4%.  Therefore the company has met its goal.

• Based on the data we are 95% confident the proportion of warranty users is between 0.9% and 3.8%.  therefore, the company has not met its goal.

• Based on the data we are 95% confident the proportion of warranty users is between 0% and 2.4%.  Therefore, the company has met its goal.