Question

2.. The SVPA sells a box of 6 Blue Hubbard pumpkins. The mean weight of all the pumpkins in the box is 14.5 lbs. The table below shows the distribution of the sample mean weight if 3 pumpkins are selected randomly from the box.

Sample Mean (lbs)	9	11	12	13	14	15	16	17	18	20
Probability	0.1	0.1	0.05	0.15	0.1	0.1	0.15	0.05	0.1	0.1

a. Suppose the three pumpkins selected are 3lbs, 9 lbs and 21 lbs. Construct a 60% confidence interval on the population mean using this sample. Explain how you figured out the margin of error.

b. Interpret the 60% confidence interval found in part a. Give the full interpretation and use the context of the problem

c. The SVPA claims that based on years of data the mean weight of the pumpkins in the box is 14.5 lbs. Does the 60% confidence interval from part a contradict this claim?

d. What is the probability the mean weight of the pumpkins in the box is in the 60% confidence interval found in part a. Explain.

e. For the hypotheses H₀: μ = 14.5 lbs and H₁: μ ≠ 14.5 lbs on the mean weight of the pumpkins in the box, what would the p-value be for the hypothesis test using the sample from part a. Use correct notation. Explain what the p-value represents within the context of the problem.

f. For the hypothesis test in part e, what would be the lowest significance level at which we would reject the null hypothesis? Explain.

Answer 1

Dear student, we can provide you with solution of four sub question at a time.

a) First we will find the mean and standard deviation of the sample given  

Here we will use T statistic to calculate the 60% confidence interval

degree of freedom: df= n-1=3-1=2

Margin of error =

b) It interprets to that we are 60% sure that mean weight of the pumpkin is between 5.386 lbs and 16.614 lbs.

c) No the confidence interval supports the claim as 14.5 lbs is well within the limits calculated above.

d) The lower and the upper limit of the confidence interval calculated above can be rounded to the nearest integer.

The limit is ( 5 , 17)

now the probability given above corresponding to the sample mean ( up till 17 lbs) is

0.1

0.1

0.05

0.15

0.1

0.1

0.15

0.05

adding these the probability is 0.80

e)

The P value is the probability of finding the observed or more extreme results when the null hypothesis of a study question is true. Hence the probability that we find mean ther than 14.5 lbs is 0.5763 when the population mean is 14.5 lbs