Statistics and Probability Answers

SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING
ASSIGNMENT QUESTION

QUESTION 2
A researcher wishes to determine whether the average amount of bleaching agent in a 1kg packet of brand X wheat flour exceeds that of brand Y. Fifteen 1kg packets of wheat flour for each brand were selected at random. It is found that on average, X contains 5% bleaching agent with a standard deviation of 0.3 and Y contains on average, 4% bleaching agent content with standard deviation of 0.5.
a) Obtain the point estimate of the mean difference of the bleaching agent content in a packet of 1kg wheat flour.
b) Determine the sampling distribution for the mean difference of the bleaching agent in a 1kg packet of wheat flour.
c) Formulate the appropriate null and alternative hypotheses to be tested.
d) Calculate the test statistics for the test.
e) Interpret your findings at 5% level of significance.

SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING

ASSIGNMENT QUESTION

QUESTION 1
A company sells packets of biscuits that they claim, on average, contains at least 20 g biscuits in each packet. They admit that their claim is wrong (and will refund any money) if a sample of 40 has a mean less than 19.8 g. If the standard deviation is 0.5 g,
a) Formulate the appropriate null and alternative hypotheses, and determine the type of test.
b) If the test is conducted at α = 0.05, determine the critical value that specify the rejection region, then complete this sentence: Reject H¬0 if test statistic is ___________________
c) Find the probability of a Type I error.
d) Find the probability of a Type II error and determine the power of test if the true mean is 19.5 g.



(3 marks)

(3 marks)


(6 marks)
(8 marks)
(Total: 20 marks)
QUESTION 2
A researcher wishes to determine whether the average amount of bleaching agent in a 1kg packet of brand X wheat flour exceeds that of brand Y. Fifteen 1kg packets of wheat flour for each brand were selected at random. It is found that on average, X contains 5% bleaching agent with a standard deviation of 0.3 and Y contains on average, 4% bleaching agent content with standard deviation of 0.5.
a) Obtain the point estimate of the mean difference of the bleaching agent content in a packet of 1kg wheat flour.
b) Determine the sampling distribution for the mean difference of the bleaching agent in a 1kg packet of wheat flour.
c) Formulate the appropriate null and alternative hypotheses to be tested.
d) Calculate the test statistics for the test.
e) Interpret your findings at 5% level of significance.






(3 marks)

(6 marks)

(2 marks)

(5 marks)
(4 marks)
(Total: 20 marks)

I have the following bills: a one dollar bill, a 2 dollar bill, a 5 dollar bill, a 20 dollar bill, and a 100 dollar bill. In how many ways can you distribute 3 bills to one person and 2 bills to a second person?

We have a box with 8 green marbles, 5 red marbles, and 7 blue marbles. We choos 3 marbles from the box at random without looking. What is the probablity that they will all be green? What is the probability they will all be blue? What is the probability they will all be red or they will all be blue? What is the probability that they will all be the same color?

what is the mean of 5 22 24 36 37 39 and 45

A company sells packets of biscuits that they claim, on average, contains at least 20 g biscuits in each packet. They admit that their claim is wrong (and will refund any money) if a sample of 40 has a mean less than 19.8 g. If the standard deviation is 0.5 g,
a) Formulate the appropriate null and alternative hypotheses, and determine the type of test.
b) If the test is conducted at α = 0.05, determine the critical value that specify the rejection region, then complete this sentence: Reject H¬0 if test statistic is ___________________
c) Find the probability of a Type I error.
d) Find the probability of a Type II error and determine the power of test if the true mean is 19.5 g.

Employees of a firm receive annual ratings. In a certain department, 4 employees received excellent ratings, 15 received good ratings, and 1 received marginal rating. If 3 employees in the department are randomly selected to complete a form for an internal study of the firm, find the probability that all 3 were rated excellent

The probability that i have to wait at the traffic lights on my way to school is 0.25,find the probability that , on two consective mornings, i have to wait on at least one morning.

The air in poultry-processing plants often contains fungus spores. Inadequate ventilation can affect the health of the workers. The problem is most serious during the summer. To measure the presence of spores, air samples are pumped to an agar plate and “colony-forming units (CFUs)” are counted after an incubation period. Here are data from two locations in a plant that processes 37,000 turkeys per day, taken on four days in the summer. The units are CFUs per cubic meter of air.


Conduct a matched pairs t-test to see if the differences in locations is significant. (note: Conduct the test so the mean difference will be positive.)
1. The value of the mean difference is (round your answer to one decimal place).

2. The standard error of the difference is (round your answer to two decimal places)

3. The degrees of freedom for this test are

4. The value of the test statistic is (round your answer to two decimal places)

5. Using an applet like this one you can find on the internet, CrunchIt, software, or you

For each of the following, find the constant c so that p(x) satisfies the condition of being a probability density function of a random variable X:
I. p(x) = c(2/3)^x, x ∈ N
II. p(x) = cx, x ∈ {1,2,3,4,5,6}