Question

Ralph’s Bookstores have indicated that the annual gross revenue for their stores has a standard deviation of σ=$50,000.

Blank #1: Given a sample size of 25 and a sample mean of $270,000, create a 90% confidence interval for estimating the population mean annual gross revenue. Enter your answer as lower bound,upper bound with no extra spaces and bounds rounded to nearest whole number.

Given a sample size of 25 and a sample mean annual gross revenue of $270,000, conduct a hypothesis test with a 0.10 level of significance to show that the population mean number of boxes sold is different from $250,000.  

Blank #2: Report the p-value of the test to 4 decimal places.

These procedures support each other because the value of $250,000 is ____________(Blank #3: not in or in) the confidence interval and the p-value of the test is ______________(Blank #4: smaller than or not smaller than) level 0.10.

Question 17 options:

Blank # 1
Blank # 2
Blank # 3
Blank # 4

Answer 1

1)

sample mean, xbar = 270000
sample standard deviation, σ = 50000
sample size, n = 25

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, Zc = Z(α/2) = 1.64

ME = zc * σ/sqrt(n)
ME = 1.64 * 50000/sqrt(25)
ME = 16400

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (270000 - 1.64 * 50000/sqrt(25) , 270000 + 1.64 * 50000/sqrt(25))
CI = (253600 , 286400)

2)

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (270000 - 250000)/(50000/sqrt(25))
z = 2

P-value Approach
P-value = 0.0455

These procedures support each other because the value of $250,000 is ( not in ) the confidence interval and the p-value of the test is(smaller than ) level 0.10.