1.Recent reports suggest that Americans plan to spend $1126 on gifts during the

Question

1.Recent reports suggest that Americans plan to spend $1126 on gifts during the holiday shopping season. You believe that Americans plan to spend less than $1126. You survey a random sample of 95 individuals and find they report planning to spend an average of $1105 on holiday gifts, with a sample standard deviation of $115.

Use the information above to conduct the appropriate hypothesis test by going through the steps we discussed in lecture. Assume the alpha level is .01 (or 1%). Fill in the following table with your answers, and be sure to show all your work.

1. What are the hypotheses?

Ho:

Ha:

2. What is the test statistic? Please compute this value and show us or explain your calculations along the way.

3. What is the p-value in this example? Please give us that specific value

4. what is your decision?

Explanation / Answer

Given that,
population mean(u)=1126
sample mean, x =1105
standard deviation, s =115
number (n)=95
null, Ho: =1126
alternate, H1: <1126
level of significance, = 0.01
from standard normal table,left tailed t /2 =2.367
since our test is left-tailed
reject Ho, if to < -2.367
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =1105-1126/(115/sqrt(95))
to =-1.7798
| to | =1.7798
critical value
the value of |t | with n-1 = 94 d.f is 2.367
we got |to| =1.7798 & | t | =2.367
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :left tail - Ha : ( p < -1.7798 ) = 0.03917
hence value of p0.01 < 0.03917,here we do not reject Ho
ANSWERS
---------------
null, Ho: =1126
alternate, H1: <1126
test statistic: -1.7798
critical value: -2.367
decision: do not reject Ho
p-value: 0.03917

we don't believe that Americans plan to spend less than $1126

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