In: Statistics and Probability
An entrepreneur examines monthly sales (in $1,000s) for 40 convenience stores in Rhode Island. (You may find it useful to reference the appropriate table: z table or t table)
Excel data
Sales | Sqft |
140 | 1810 |
160 | 2500 |
80 | 1010 |
180 | 2170 |
140 | 2310 |
110 | 1320 |
90 | 1130 |
110 | 1500 |
130 | 1950 |
80 | 1010 |
110 | 1770 |
140 | 1840 |
140 | 2330 |
140 | 2490 |
120 | 1550 |
120 | 1900 |
210 | 2320 |
120 | 1700 |
180 | 2500 |
170 | 2380 |
160 | 1880 |
120 | 1780 |
120 | 1610 |
90 | 1230 |
140 | 1920 |
100 | 1260 |
90 | 1260 |
190 | 2470 |
130 | 2420 |
110 | 1550 |
100 | 1260 |
140 | 2230 |
100 | 1500 |
140 | 1970 |
120 | 1530 |
120 | 1800 |
110 | 1520 |
170 | 2210 |
100 | 1440 |
110 | 1470 |
a. Select the null and the alternative hypotheses in order to test whether average sales differ from $130,000.
H0: μ = 130,000; HA: μ ≠ 130,000
H0: μ ≥ 130,000; HA: μ < 130,000
H0: μ ≤ 130,000; HA: μ > 130,000
b-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
b-2. Find the p-value.
p-value < 0.01
0.01 ≤ p-value < 0.02
0.02 ≤ p-value < 0.05
0.05 ≤ p-value < 0.10
p-value ≥ 0.10
c. At α = 0.05 what is your conclusion? Do average sales differ from $130,000?
Reject H0; average sales differ from $130,000.
Reject H0; average sales do not differ from $130,000.
Do not reject H0; average sales differ from $130,000.
Do not reject H0; average sales do not differ from $130,000.
Values ( X ) | ||
140000 | 138062500 | |
160000 | 1008062500 | |
80000 | 2328062500 | |
180000 | 2678062500 | |
140000 | 138062500 | |
110000 | 333062500 | |
90000 | 1463062500 | |
110000 | 333062500 | |
130000 | 3062500 | |
80000 | 2328062500 | |
110000 | 333062500 | |
140000 | 138062500 | |
140000 | 138062500 | |
140000 | 138062500 | |
120000 | 68062500 | |
120000 | 68062500 | |
210000 | 6683062500 | |
120000 | 68062500 | |
180000 | 2678062500 | |
170000 | 1743062500 | |
160000 | 1008062500 | |
120000 | 68062500 | |
120000 | 68062500 | |
90000 | 1463062500 | |
140000 | 138062500 | |
100000 | 798062500 | |
90000 | 1463062500 | |
190000 | 3813062500 | |
130000 | 3062500 | |
110000 | 333062500 | |
100000 | 798062500 | |
140000 | 138062500 | |
100000 | 798062500 | |
140000 | 138062500 | |
120000 | 68062500 | |
120000 | 68062500 | |
110000 | 333062500 | |
170000 | 1743062500 | |
100000 | 798062500 | |
110000 | 333062500 | |
Total | 5130000 | 37177500000 |
To Test :-
H0: μ = 130,000
HA: μ ≠ 130,000
Test Statistic :-
t = -0.3585
Test Criteria :-
Reject null hypothesis if
Result :- Fail to reject null hypothesis
b-2. Find the p-value.
P value
Looking for the value t = 0.3585 across n - 1 = 40 - 1 = 39 degree of freedom for two tailed
t = 0.3585 lies between value 0.000 and 0.681 respective P value is 1.00 and 0.50
P value = 0.05 ≤ p-value < 0.10
c. At α = 0.05 what is your conclusion? Do average sales differ from $130,000
Do not reject H0
Average sales do not differ from $130,000.