If n15 and p04 then the standard deviation of the binomial

Question

Question 1. If n=15 and p=0.4, then the standard deviation of the binomial distribution is 3.6.

True
False

Question 2. If the level of confidence and sample size remain the same, a confidence interval for a population proportion p will be narrower when p(1-p) is larger than when it is smaller.

True
False

Question 3. In a simple linear regression model, the coefficient of determination not only indicates the strength of the relationship between independent and dependent variable, but also shows whether the relationship is positive or negative.

True
False

Question 4. The sample standard deviation s is an unbiased estimator of the population standard deviation.

True
False

Question 5. If the random variable of x is normally distributed, 68.26% of all possible observed values of x will be within two standard deviations of the mean.

True
False

Question 6. If n=20 and p=.4, then the mean of the binomial distribution is 8

True
False

Question 7. First a confidence interval is constructed without using the finite population correction factor. Then, for the same identical data, a confidence interval is constructed using the finite population correction factor. The width of the interval with the finite population correction factor is wider than the confidence interval without the finite population correction factor.

True
False

Question 8. The power of a statistical test is the probability of rejecting the null hypothesis when it is true.

True
False

Question 9. The sampling distribution of the sample mean is developed by repeatedly taking samples of size n and computing the sample means and reporting the resulting sample means in the form of a probability distribution.

True
False

Question 10. For a continuous distribution, the exact probability of a particular value is always zero.

True
False

Question 11. As the level of significance α increases, we are more likely to reject the null hypothesis.

True
False

Question 12. If events A and B are mutually exclusive, then P(A|B) is always equal to zero.

True
False

Question 13. If p=.9 and n=40, then we can conclude that the sampling distribution of the proportions is approximately a normal distribution.

True
False

Question 14. The standard deviation of the sampling distribution of the sample mean is the same as the population standard deviation.

True
False

Question 15. If events A and B are mutually exclusive, then P(A and B) is always equal to zero.

True
False

Question 16. If a null hypothesis is rejected at a significance level of .01, it will ______ be rejected at a significance level of .05

Always
Sometimes
Never

Question 17. The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue. The historical records of the company show that over the past 8 years 14 percent of the accounts are delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts. What is the probability that at least 30 accounts will be classified as delinquent?

31.86%
18.14%
81.86%
63.72%
75.84%

Question 18. The price-to-earning ratio for firms in a given industry is distributed according to normal distribution. In this industry, a firm with a standard normal variable value of Z=1:

Has an above average price-to-earning ratio
Has an below average price-to-earning ratio
Has an average price-to-earning ratio
May have an average or below average price-to-earnings ratio

Question 19. In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a standard deviation of .3 inches. What is the 95% confidence interval for the true mean length of the bolt?

2.904 to 3.396
2.308 to 3.692
2.412 to 3.588
2.770 to 3.231
2.884 to 3.086

Question 20. The point estimate of the variance in a regression model is

SSE
β(0)
β(1)
MSE

Question 21. The mean life of pair of shoes is 40 months with a standard deviation of 8 months. If the life of the shoes is normally distributed, how many pairs of shoes out of one million will need replacement before 36 months?

500,000
808,500
191,500
308,500

Question 22. When determining the sample size, if the value found is not an integer initially, the next highest integer value will ____________ be chosen.

Always
Sometimes
Never

Question 23. The _______ of two events X and Y is another event that consists of the sample space outcomes belonging to both event X and Y.

Sample space outcome
Conditional Probability

Complement of events
Long-run relative frequency
Intersection

Question 24. A multiple-choice test has 30 questions and each one has five possible answers, of which one is correct. If all answers were guesses, find the probability of getting exactly four correct answers.

0.0604
0.1325
0.2552
0.8000

Question 25. A standard normal distribution has a mean of _____ and standard deviation of _____.

Zero, Zero
Zero, One
One, One
One, Zero

Question 26. The average customer waiting time at a fast food restaurant has been 7.5 minutes. The customer waiting time has a normal distribution. The manager claims that the use of a new system will decrease average customer waiting time in the store. What is the null and alternative hypothesis for this scenario?

H₀:∝ =7.5 and H_A: ∝≠ 7.5
H₀:∝ ≤ 7.5 and H_A: ∝ > 7.5
H₀:∝ ≥ 7.5 and H_A: ∝ < 7.5
H₀:∝ <7.5 and H_A: ∝≥ 7.5
H₀:∝ > 7.5 and H_A: ∝ ≤ 7.5

Question 27. If the wages of workers for a given company are normally distributed with a mean of $15 per hour, then the proportion of the workers earning more than $13 per hour:

Is less than the proportion earning less than $13 per hour
Is equal to the proportion earning less than $13 per hour
Is greater than the proportion earning less than $13 per hour
Is less than 50%
Cannot tell from the information given.

Question 28. In a study conducted by UCLA, it was found that 25% of college freshmen support increased military spending. If 6 college freshmen are randomly selected, find the probability that: "fewer than 4 support increased military spending"

0.9624
0.9954
0.7844
0.0330

Question 29. When the level of confidence and the sample size remain the same, a confidence interval for a population mean µ will be ________________, when the sample standard deviation s is smaller than when s is larger.

Wider
Narrower
Sometimes wider, sometimes narrower.
They will be the same

Question 30. Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. One item is drawn from each container: What is the probability that one of the items is defective? (Hint: you have to use both rule of addition and rule of multiplication/conditional probability rules)

Question 31. Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25% for University A and 40% for University B. What is the probability that Joe will be accepted at one and only one university?

Question 32. The probability that an appliance is in repair is .5. If an apartment complex has 100 such appliances, what is the probability that at least 60 will be in repair? Use the normal approximation to the binomial.

Question 33. The J.O. Supplies Company buys calculators from a Korean supplier. The probability of a defective calculator is 10%. If 100 calculators are selected at random, what is the standard deviation of the number of defectives?

Question 34. A random sample of size 36 from a normal population yields mean X-bar = 32.8 and standard deviation s = 4.51. Construct a 95 percent confidence interval for μ.

Question 35. Employees of a local university have been classified according to gender and type of job as follows:

Job                      Male    Female

Faculty                 110       10
Salaried staff         30        50
Hourly staff            60        40

If an employee is selected at random, what is the probability that the employee is a female or works as an hourly staff?

Question 36. A microwave manufacturing company has just switched to a new automated production system. Unfortunately, the new machinery has been frequently failing and requiring repairs and service. The company has been able to provide its customers with a completion time of 6 days or less. To analyze whether the completion time has increased, the production manager took a sample of 25 jobs and found that the sample mean completion time was 6.5 days with a sample standard deviation of 1.5 days. At a significance level of .05, test whether the completion time has increased. (form the hypotheses, show the critical and calculated values of the test statistic and perform the test)

Question 37. An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that: Fewer than two troubles will be repaired on the same day?

Answer 1

Choose the answer of given questions as true or false. Question 1. If n=15 and p=0.4, then the standard divergence of the binomial distribution is 3.6. i. True ii. False Question 2. If the level of confidence and sample size remain the same, a confidence interval for a population proportion p will be narrower when p(1-p) is larger than when it is smaller. i. True ii. False Question 3. In a simple linear regression model, the coefficient of determination not only designates the strength of the association between independent and dependent variable, but as well illustrates whether the relationship is positive or negative. i. True ii. False