Statistics and Probability Answers

Suppose that at a busy traffic junction, the probability p of an individual car having
an accident is 0.0001. During a certain part of the day, 100 cars pass through the
junction. What is the probability of two or more cars being involved in an accident
within this period?

QUESTION 3 Jay –Ethan Company is a multi-billion pharmaceutical company that has won a contract by the government to produce hand sanitizers and respiratory gadgets for frontline health workers in Bono East region. As a result, the company has decided to give bonuses to its employees to motivate them for the risky task ahead. A sample of the weekly bonus received by the employees is organized in the table below: Weekly Bonus ($) 30<35 35<40 40<45 45<50 50<55 55<60 60<56 65<70 Number of employees(f) 8 6 10 5 15 4 9 3 NB: Approximate to 2 decimal places i) Find the mean amount of bonus given to the employees. ii) Calculate the standard deviation and interpret it. iii) What is the modal amount paid? iv) Would you say the bonus distribution follows the standard normal distribution? Why? v) Calculate the coefficient of variation for the bonus distribution of Jay-Ethan and compare it with the coefficient of variation of 19.45% for the bonus distribution of KGH, a subsidiary of Jay-Ethan.

W2

1. SAT scores are distributed with a mean of 1,500 and a standard deviation of 300. You are interested in estimating the average SAT score of first year students at your college. If you would like to limit the margin of error of your 98% confidence interval to 40 points, at least how many students should you sample?


A. 131
B. 216
C. 217
D.306

7. If it’s relatively riskier to reject the null hypothesis when it might be true, should a smaller or a larger significance level be used?

A. smaller
B. larger

part 2

1. An insurance company is reviewing its current policy rates. When originally setting the rates they believed that the average claim amount was $1,800. They are concerned that the true mean is actually higher than this, because they could potentially lose a lot of money. They randomly select 40 claims, which yield a sample mean of $1,950. Which of the following is the correct set of hypotheses for this scenario?


A. H_0: x bar = 1,800
H_A: x bar > 1,800

B. H_0: μ=1,800
H_A: :μ>1,800

C. H_0 :μ=1,950
H_A: μ>1,800

D.H_0: μ=1,800
H_A :μ>1,950

3. Two-sided alternative hypotheses are phrased in terms of:

A. ≤ or ≥
B. ≈ or =
C. < or >
D. ≠

4. A Type 1 error occurs when the null hypothesis is

A. not rejected when it is true
B. not rejected when it is false
C. rejected when it is true
D. rejected when it is false

Inferential.

A company offering online speed reading courses claims that students who take their courses show a 5 times (500%) increase in the number of words they can read in a minute without losing comprehension. A random sample of 100 students yielded an average increase of 415% with a standard deviation of 220%.

Calculate a 95% confidence interval for the average increase in number of words students can read in a minute without losing comprehension. Choose the closest answer.

A. (371.88, 458.12)
B.(378.7, 451.3)
C.(411.37, 418.63)
D.(412.09, 417.91)

inferential

6. Suppose we collected a sample of size n = 100 from some population and used the data to calculate a 95% confidence interval for the population mean. Now suppose we are going to increase the sample size to n = 300. Keeping all else constant, which of the following would we expect to occur as a result of increasing the sample size?

1. The standard error would decrease.
2. Width of the 95% confidence interval would increase.
3. The margin of error would decrease.

A. II and III
B. I and III
C.I and II
D.I, II, and III

inferential.

4. Which of the following is false about the central limit theorem (CLT)?

A. As the sample size increases, the sampling distribution of the mean is more likely to be nearly normal, regardless of the shape of the original population distribution.

B. The CLT states that the sampling distribution will be centered at the true population parameter.

C. If the population distribution is normal, the sampling distribution of the mean will also be nearly normal, regardless of the sample size.

D. If we take more samples from the original population, the sampling distribution is more likely to be nearly normal.

Inferential.

1. We want to estimate the average coffee intake of Coursera students, measured in cups of coffee. A survey of 1,000 students yields an average of 0.55 cups per day, with a standard deviation of 1 cup per day. Which of the following is not necessarily true?

A. The sample distribution is right skewed.
B.0.55 is a point estimate for the population mean.
C. μ=0.55, σ=1
D. x bar = 0.55, s=1

2. The standard error measures:

A. the variability of the sampled observations
B.the variability in the population
C. the variability of population parameters
D.the variability of sample statistics

6. At any given time about 5.5% of women (age 15-45) are pregnant. A home pregnancy test is accurate 99% of the time if the woman taking the test is actually pregnant and 99.5% accurate if the woman is not pregnant. If the test yields a positive result, what is the posterior probability of the hypothesis that the woman is pregnant?
A. 0.08
B. 0.99
C. 0.995
D. 0.92

7. Your boss is a biologist who needs wood samples from long-leaf pine trees with a fungal disease which is only visible under a microscope, and she sends you on an assignment to collect the samples. She wants at least 50 different diseased samples. She tells you that approximately 28% of long-leaf pine trees currently have the fungal disease. If you sample 160 long-leaf pine trees at random, what is the probability you’ll have at least 50 diseased samples to return to your boss?

A. 92%

B. 28%

C.13%

D. 82%


18%

a study claims that 98.6F is the average if the normal room temperature. The sample of body temperature for 25 houses are recorded in the figure. By using alpha = 0.05, can the claim be rejected
97.8 97.2 97.4 97.6 97.8
97.9 98.0 98.0 98.0 98.1
98.2 98.3 98.3 98.4 98.4
98.4 98.5 98.6 98.6 98.7
98.8 98.8 98.9 98.9 99.0