A group of young businesswomen wish to open a clothing store in particular area,
ID: 3125379 • Letter: A
Question
A group of young businesswomen wish to open a clothing store in particular area, but only if the average income of households in the area is at least $122,000. A random sample of 10 households showed the following results (the numbers are in the thousands of dollars):
118, 119, 119, 119, 116, 117, 121, 127, 121, 122
The businesswomen are worried that the average income is below the target income threshold.
a) What hypotheses should these businesswomen test if their concern is that the average household income is below $122,000?
b) What distribution would they use to find the CRITICAL value for this test?
c) At the 5% level of significance, what is the CRITICAL value?
d) What is the CALCULATED value for this test?
e) Should the women locate the business in this area? Why?
Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u >= 122
Ha: u < 122 [ANSWER]
*******************
b)
As we only have n = 10, we use the T DISTRIBUTION. [ANSWER]
**********************
c)
As we can see, this is a left tailed test.
Thus, getting the critical t, by table/technology,
df = n - 1 = 9
tcrit = - 1.833112933 [ANSWER]
*************************
c)
Getting the test statistic, as
X = sample mean = 119.9
uo = hypothesized mean = 122
n = sample size = 10
s = standard deviation = 3.107338983
Thus, t = (X - uo) * sqrt(n) / s = -2.137128624 [ANSWER]
**********************
e)
As t < -1.83311, we REJECT THE NULL HYPOTHESIS.
Hence, there is significant evidence taht the mean income is below $122000 at 0.05 level. Therefore, the women should not locate the business in this area.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.