Twelve students are randomly sampled from (n) University. The amount of money, i

Question

Twelve students are randomly sampled from (n) University. The amount of money, in dollar, they spent to buy a pair of shoes is given below: 208,203,198,200,199,201,202,209,204,206,205,207. Does the average amount of money students in university spent to buy a pair of shoe exceeds $ 200? Assume that the amounts of money all students spent follow a normal distribution.

a. Define the variable in question Is it discrete or continuous?

b. What are the average and variance of the amount of money all students spend to buy a pair of shoes?

c. Write out the information on the population in question.

d. Write out the relevant information on the given sample.

e. What is the aim here?

f. How much cost of a pair of shoe bought by any 12 student, on an average, is too much?

g. What value of based on any 12 student is too much?

h. Decide on the average cost of a pair of shoe (bought by all students) by sample average.

i. Decide on the average cost of a pair of shoe (bought by all student) using t-statistics

Explanation / Answer

a. Define the variable in question Is it discrete or continuous?

Here the variable is question is continous.

b.  What are the average and variance of the amount of money all students spend to buy a pair of shoes?

Answer : Avereage aamount spend = $ 203.5

Variance = $ 13

c.  Write out the information on the population in question.

Answer : Here population in question is the amount of money students in the given university spent to buy a pair of shoe is the population here. We assume that amount is in normal distribution.

d. Write out the relevant information on the given sample.

Answer: Here sample size is 12 and we have calculated its mean and sample varaince.

Standard error of sample mean = /sqrt(n) = 13/sqrt(12) = 1.0408

e. How much cost of a pair of shoe bought by any 12 student, on an average, is too much?

Answer : Here for any group of 12 student on an average if spend more than 1.645 standard error if spend then it is too much.

SO the too much amount is = 200 + 1.645 * 1.0408 = $ 201.71

Here we take 1.645 as 95% percentile cutoff for expensive shoes.

h. Decide on the average cost of a pair of shoe (bought by all students) by sample average.

Here we can decide that as average cost is higher than too much high cost than we can say that the average amount of money students in university spent to buy a pair of shoe exceeds $ 200.

i. Decide on the average cost of a pair of shoe (bought by all student) using t-statistics

t = (203.5 - 200)/ 1.0408 = 3.3628

Here for dF = 11 and alpha = 0.05

tcrtical = 2.2

so here t > tcritical so we shall say that the average amount of money students in university spent to buy a pair of shoe exceeds $ 200.

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