Proportions
A small college has a population of 1200 students and 12% of them are overweight. A sample of 200 randomly selected students was taken and 8% of them were overweight. Why is it inappropriate to use sampling distribution of the sample proportion for this sample?
The sample size is greater than 10% of the population
Which of the following will increase the width of a confidence interval?
Increasing the confidence level
Decreasing the confidence level
Increasing the sample size
Increasing the confidence level
A recruiting firm reported that 78% of U.S. companies use social networks to recruit job candidates. In a random sample of 220 companies, 81% used social networks for recruiting. Does this provide enough evidence to show that the claim of the recruiting firm is wrong? Identify the appropriate null and alternative hypotheses.
Ho: p = 0.78
Ha: P ≠ 0.78
A biologist studying environmental pollutants finds that 32% of a random sample of tuna has high levels of mercury in their blood. The 98% confidence interval is found to be (0.23, 0.41). What is the level of significance of the above hypothesis test?
0.02
Suppose 25% of American adults meet the surgeon general's recommendation for daily physical activity. If a random sample of 10 American adults is taken, what are the mean and standard deviation of the proportion that meet the surgeon general's recommendation?
μ = 0.25
σ = 0.1369
A 95% confidence interval for the proportion of U.S. adults who say that they take vitamin E as a supplement is (0.304, 0.326). What is the margin of error?
0.011
In testing the hypotheses (Ho: p = 0.32, Ha: p ≠ 0.32) the test statistic is found to be 2.14. What is the correct p-value?
0.0324
True or False: For a given sample size, higher confidence means a smaller margin of error.
False
According to a recent survey, 53% of adults say they never wear a helmet when riding a bike. Suppose we randomly select 180 adults and find 59% of the sample say they never wear a helmet when riding a bike. Correctly describe the distribution for the proportion of adults in the sample who never wear a helmet when riding a bike.
p̂ ~ AN (0.53, 0.0372)
A survey was conducted to determine the proportion of adults who approve of attempts to clone a human. Based on the response of 1000 adults a 90% confidence interval was calculated to be (0.09, 0.13). What can be concluded?
We are 90% confident that the population proportion of adults who approve of attempt to clone a human is between 0.09 and 0.13.
A biologist studying environmental pollutants finds that 32% of a random sample of tuna has high levels of mercury in their blood. The 98% confidence interval is found to be (0.23, 0.41). A researcher has claimed that 45% of tuna has high levels of mercury. What can we conclude if we use the above confidence interval to test the claim?
Since 0.45 does not fall in the confidence interval the researcher's claim is incorrect.
In hypothesis testing, a type II error is failing to reject a false hypothesis.
True
A survey of U.S. workers found that 79% rely on their own vehicle to get to work. A random sample of 250 workers is selected. In the sample, 72% said they rely on their own vehicle to get to work. Describe the distribution of the proportion of workers in the sample who rely on their vehicle to get to work.
p̂ ~ AN (0.79, 0.0258)
In a survey of 250 U.S. adults, 197 say they pay the majority of their bills online. What is a 98% confidence interval for the population proportion of adults that say that pay the majority of their bills online?
(0.7279, 0.8481)
A researcher claims that 45% of students drop out of college. He conducts a hypothesis test and fails to reject the null hypothesis. What is the correct interpretation of the conclusion?
There is not sufficient evidence to reject the claim that 45% of students drop out of college.
Many consumers pay careful attention to state nutritional contents on packaged foods when making purchases. It is important that the information on packages be accurate. The stated calorie content on a frozen dinner package is 240. A random sample of 12 frozen dinners of a certain type was selected and used to test this null hypothesis. Describe a type II error.
We conclude that the mean calorie content of the dinners is 240 when it is different from 240.
A survey of U.S. workers found that 79% rely on their own vehicle to get to work. A random sample of 250 workers is selected. In the sample, 72% said they rely on their own vehicle to get to work. What is the probability that no more than 72% of the sample rely on their own vehicle to get to work?
0.0033
A random survey of 385 adults found that 114 had attended a religious service to commemorate the anniversary of the attacks on the World Trade Center. What is a 99% confidence interval for the population proportion of adults who attended a religious service to commemorate the attacks?
(0.2362, 0.3560)
A hypothesis test was conducted to test whether more than 50% of recent college graduates had a job offer prior to graduation. A test statistic of z = 1.59 was found. When testing at the 5% significance level, what is the most appropriate conclusion?
There is not sufficient evidence to conclude more than 50% of recent college graduates had a job offer prior to graduation.
A pollster is going to sample voters in a large city to estimate the proportion who support the incumbent candidate for mayor. He wishes to estimate the proportion to within 4.5% with 95% confidence. How many adults should be included in the sample?
475