Question

Retail Store	Deluxe	Standard
1	44	33
2	43	30
3	41	28
4	33	20
5	32	19
6	42	30
7	43	33
8	30	18

The selling prices (in $) for the deluxe and standard model Ryobi wood sanders are shown for a sample of eight retail stores. Does the data suggest the difference in average selling price of these Ryobi models is more than $10 at α=0.01?

For the hypothesis stated above (in terms of Deluxe - Standard):

Questions 1
What is the test statistic? ______

Questions 2
What is the conclusion? (Choose TISETC or TINSETC) µDeluxe - µStandard (Choose >,<, =)______

Questions 3
What is the p-value? Fill in only one of the following statements.

If the Z table is appropriate, p-value =______

If the t table is appropriate, ______< p-value <______

Answer 1

For Deluxe :  

Sample mean using excel function AVERAGE(), x̅1 = 38.5

Sample standard deviation using excel function STDEV.S, s1 = 5.7817

Sample size, n1 = 8

For Standard :  

Sample mean using excel function AVERAGE(), x̅2 = 26.375

Sample standard deviation using excel function STDEV.S, s2 = 6.3457

Sample size, n2 = 8

Null and Alternative hypothesis:

Ho : µ1 - µ2 ≤ 10

H1 : µ1 - µ2 > 10

Q1 :

Pooled variance :

S²p = ((n1-1)*s1² + (n2-1)*s2² )/(n1+n2-2) = ((8-1)*5.7817² + (8-1)*6.3457²) / (8+8-2) = 36.8482

Test statistic:

t = (x̅1 - x̅2) / √(s²p(1/n1 + 1/n2 ) = (38.5 - 26.375) / √(36.8482*(1/8 + 1/8)) = 0.7001

df = n1+n2-2 = 14

Critical value :

Right tailed critical value, t crit = ABS(T.INV(0.01, 14)) = 2.624

Decision:

As t < 2.624, Do not reject the null hypothesis

Q2:

TINSETC µ_deluxe - µ_standard > 10

Q3:

p-value :

Right tailed p-value = T.DIST.RT(0.7001, 14) = 0.2477

0.20 < p -value < 0.50