Probability
Consider a box containing 15 identical pens. It is known that 5 of the 15 pens are defective. Two pens are selected at random, without replacement. What is the mean? (create a probability distribution)
0.689
A data set has a normal distribution, a standard deviation of 3.5, and 4% of the data is less than 20. What is the mean?
26.125
A local restaurant keeps records of reservations and no shows. In a random sample of 150 Saturday reservations, it is found that 70 of them are no shows.
What is the sample proportion of no shows?
Find a 95% confidence interval for the true proportion of Saturday no shows.
1. 0.4667
2. (0.3868, 0.5465)
A pharmaceutical company’s old antacid formula provided relief for 70% of the people who used it. The company tests a new formula to see if it is better and the p-value is calculated to be 0.027. What 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
In testing the hypothesis Ho: p=0.3 Ha: p is not equal to 0.3
the test statistic is found to be 2.11. Which of the following is the correct p-value?
0.0348
In the last quarter of 2008, a group of 64 mutual funds had a mean return of 2.4% with a standard deviation of 5.6%. Assume the return on the group of funds follows a normal distribution (use the empirical rule) The worst 2.5% will have a return of less than what amount?
-8.8
87% of high school students earn a diploma. A random sample of 1600 students are selected. Describe the distribution of proportion.
ṕ ~ AN (0.87, 0.0084)
A high school is doing a study on the number of students who actually do their homework. In a random sample of 300 kids, it is found that 100 actually do all of their homework regularly.
What is the sample proportion of students who do their homework?
Find a 90% confidence interval for the true proportion.
1. 0.33
2. (0.2886, 0.3781)
A survey was conducted to estimate the proportion of adults who are obese. A 95% confidence interval was calculated to be (0.19, 0.24). Which of the following best interprets the confidence interval?
We can be 95% confident that the population proportion of adults who are obese is between 0.19 and 0.24
If we fail to reject a null hypothesis at level of significance (alpha) then the hypothesis test is statistically significant at level (alpha)
true/false
false
A mortality rate for certain disease is 25%. A random sample of twelve patients with this disease is selected. What is the probability that exactly half of the patients selected will die from the disease?
.040
A data set follows normal distribution and has a mean of 100, a standard deviation of 21. Use the empirical rule. 84% fall above what value?
79
What are two ways to get a narrower confidence interval for a proportion?
Increase sample size and decrease confidence level
A politician is trying to decide whether to vote for a new tax bill that calls for substantial reforms. He will only vote for the bill if he believes that more than 50% of voters in his district support the bill. A random sample of voters in his district is used to test the following hypotheses: Ho: p = 0.5 vs Ha: p > 0.5 What would be a type II error?
The politician does not believe more than 50% of voters in his district support the bill so he votes against it, and the bill is supported by the majority of voters
The power of a hypothesis test is the probability we reject the null hypothesis when the null hypothesis is false
true/false
true
A mortality rate for certain disease is 25%. A random sample of twelve patients with this disease is selected. What is the probability that at least two of the twelve patients will die from the disease?
.842
A survey was conducted to estimate the proportion of adults who say it is acceptable to check personal email while at work. A 95% confidence interval was calculated to be (0.633, 0.691).
Identify the point estimate of the true proportion
Identify the margin of error for the above confidence interval
1. 0.662
2. 0.029
A researcher wishes to estimate the population proportion of U.S. adults who are overweight. They wish to estimate the proportion to within 4.5 % with a 95% confidence interval. How many U.S. adults should be included in the sample?
475
A company’s old antacid formula provided relief for 70% of the people who used it. A hypothesis test whether a new antacid formula is better. The p-value is calculated to be 0.07. Which of the following is the correct conclusion and reason for the conclusion (use a 0.05 level of significance)?
Fail to reject the null hypothesis because the p-value is larger than the significance level of the test
Which of the following are true statements?
A small p- value implies strong evidence against the null hypothesis
The p-value is the probability that the null hypothesis is true
If we reject the null hypothesis, it must be false
A only
B only
C only
A and b are true statements
None of the above are true statements
1
The weight of a certain breed of dog follows a normal distribution with a mean of 100 pounds and a standard deviation of 21. What percentage of dogs weigh between 121 and 163 pounds? (use the empirical rule)
15.85
A survey was conducted to estimate the proportion of adults who view teaching as a prestigious profession. A 95% confidence interval was calculated to be (0.459,0.521)
Identify the point estimate of the true proportion
Identify the margin of error for the above confidence interval
1. 0.49
2. 0.031
A random survey of 375 women found 294 said they change their nail polish once a week. What is a 90% confidence interval for the population proportion?
(0.74, 0.819)
A recruiting firm reported that 78% of 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 null and alternative
Ho: p=0.78
Ha: p not equal to 0.78
Data is collected to test the hypotheses Ho: p=0.5 vs Ha: p doesn't equal 0.5. You obtain a p-value of 0.022. Will a 99%, 95%, or 90% confidence interval include the value of 0.5
99%