Hypothesis Testing
In testing the hypotheses Ho: p = 0.6, Ha: p < 0.6
The test statistic is found to be 2.09. Which of the following is the correct p-value?
0.0183
A large monkey house at a zoo has a population of 950 monkeys and 12% of them are overweight. A sample of 200 randomly selected monkeys was taken and the number overweight was counted. Why is it inappropriate to use the normal approximation to the binomial for this situation?
The sample size is greater than 10% of the population.
Flat screen TVs require high-quality glass with very few flaws. A television manufacturer inspected the glass panels received from its supplier. It was found that 48% of panels had no flaws, 27% of panels had one flaw, 16% had two flaws and 9% had three flaws. Calculate the standard deviation of the number of flaws in a glass panel received from this supplier.
0.99
Given the following Confidence Interval, calculate the Point Estimate:
(0.3046, 0.6782)
0.49
A random survey of 495 adults found that 59 had diabetes. Which of the following is a 98% confidence interval for the population proportion of adults with diabetes?
(0.0853,0.1531)
A 2011 Rasmussen poll of 650 adults showed that 53% opposed having students
attending school year-round without the traditional summer break. Is there enough
evidence to show more than 50% of adults oppose year-round school?
Identify the appropriate null and alternative hypotheses.
Ho: p = 0.5 Ha: p > 0.5
The amount of cheese on a randomly selected medium pizza is normally distributed with a mean of 0.53 pounds and a standard deviation of 0.027 pounds. What is the probability that the amount of cheese on a medium pizza is between 0.55 and 0.6 pounds?
0.2248
The gas mileage for a new model of car in normally distributed, with a standard deviation of 3.5 miles per gallon. If only 4% of the cars have a gas mileage of less than 20 mpg, what is the mean of the distribution?
26.125
Given the following confidence interval, calculate the margin of error:
(0.1385, 0.8902)
0.38
According to the State Department, only twenty-seven percent of Americans carry a valid passport. Suppose we take a random sample of 11 Americans. Which of the following best describes the distribution of X=number of Americans that carry a valid passport?
X ~ B(11, 0.27)
Which of the following are true statements?
I. A small p-value implies strong evidence against the null hypothesis.
II. The p-value is the probability that the null hypothesis is true.
III. If we reject the null hypothesis, it must be false.
I only
Suppose it is known that 87% of young Americans earn a high school diploma. A random sample of 1600 young Americans is selected.
Describe the distribution of the proportion of people in the sample who have earned their high school diploma.
pˆ ~ AN(0.87,0.0084)
Suppose it is known that 87% of young Americans earn a high school diploma. A random sample of 1600 young Americans is selected.
What is the probability that at least 88% of the sample of 1600 young Americans will have earned their high school diploma?
0.1170
What are two ways to get a narrower confidence interval for a proportion?
- increase the sample size
- decrease the confidence level
A lab technician runs a test to check whether a piece of medical equipment is functioning
properly (the null hypothesis is that the equipment is functioning properly). Which of the
following describes a Type I error for this test?
The technician decides the equipment is not functioning properly, but it is.
The death rate from a particular form of cancer is 23% during the first year. A new medication is tested to see if it reduces the first year mortality rate and the p-value is calculated to be 0.042. Which of the following is the correct conclusion and reason for the conclusion? (use a 0.05 level of significance)
Reject the null hypothesis because the p-value is smaller than the significance level of the test.
The length of a newborn harbor seal follows a normal distribution with a mean length of
29.5 inches and standard deviation 1.2 inches. What is the probability that a randomly selected newborn seal is less than 27 inches long?
0.0188
In Mexico, 70% of drivers who are arrested for driving while intoxicated (DWI) are convicted. Suppose 15 independently selected drivers are arrested for DWI. What is the probability that at least 14 of the 15 drivers are convicted?
0.0353
A random survey of 495 adults found that 59 had diabetes. Which of the following is a 98% confidence interval for the population proportion of adults with diabetes?
(0.0853,0.1531)
A medical researcher estimates the percentage of children who are exposed to lead based paint, adding that his estimate has a margin of error of about 3% meaning that:
A) He is confident the true proportion is within ±3% of his estimate
B) He is confident that 97% of the population falls under his estimate
C) He is confident the true proportion is within ±1.5% of his estimate
D) He is confident the true proportion is more than ±3% from his estimate
A) He is confident the true proportion is within ±3% of his estimate
A survey was conducted to determine the proportion of adults who rate the economy as good. Based on the responses of a random sample of adults a 96% confidence interval was calculated to be (0.198, 0.251).
Since 0.20 falls in the confidence interval, we do not have enough evidence to reject the claim.
The length of a newborn harbor seal follows a normal distribution with a mean length of 29.5 inches and standard deviation 1.2 inches. What is the value of the first quartile of newborn seal lengths?
28.696
According to a 2010 article, 20% of driver’s license applicants fail the written test in
Illinois. If a random sample of 750 driver’s license applicants in Illinois is selected, what is the probability no more than 160 fail the written test?
0.8186
A catalog sales company promises to deliver Internet orders within three days. A survey was conducted to determine the proportion of Internet orders that arrive on time. Based on the response of 1200 randomly selected customers a 95% confidence interval was calculated to be (0.82, 0.94).
What is the correct interpretation for this confidence interval?
We are 95% confident that the population proportion of orders that arrive on time is between 0.82 and 0.94.
A polling agency wants to determine the percentage of voters in favor of extending tax cuts. They wish to estimate the percent to within 2% with 95% confidence. How many individuals should be included in the sample?
2401