Question

This is to be done in excel (which I can do), but I am confused about which tail test to use and why to accept or reject H0- and the summary.

According to research, holiday shoppers spent an average of $370 over a holiday weekend in 2008. The accompanying data show the amount spent by a random sample of holiday shoppers during the same weekend in 2009. Retailers were concerned that the economic downturn was affected holiday sales. Does this sample support these concerns using α = 0.10? The hypotheses are H0: μ ≥ 370 and H1: μ < 370. (6 points total)

Shopping $ 420 276 375 239 225 208 354 436 382 395 319 67 415 425 374 282

a) Excel does not have a built in one sample t-test so we will need to trick it. First copy the data below the
previous problem (I used cell A26, change your cell references according to where you put your data)
including the label. In the column next to the data we will need a column of zeros labeled Variable 2. Then
select Data Analysis, then t-test: Paired Two-Sample for Means, then OK. See screen shots below.
Move your curser to the Variable 1 Range box, then using your mouse select the data including the
label. Click into the Variable 2 Range box and use your mouse to select the column of zeros including
the label. Type in the hypothesized mean difference of 370. Check the Labels box and change alpha to
fit the problem. Select the circle next to Output Range, move your curser into the box to the right of
Output Range, then use your mouse to select cell c26. Select OK.

b) Highlight the test statistic in blue. (0.5 point)
c) Highlight the correct p-value in yellow. Be careful to look at whether you are doing a one or two tailed
test. (0.5 point)
d) To the right of the table, type in your decision of either reject or do not reject H0. (1 point)
e) Type in your summary using context and units of the problem. (2 points)

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u > 370
Alternative hypothesis: u < 370

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.10. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 25.435
DF = n - 1

D.F = 15
t = (x - u) / SE

t = - 1.789

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of -1.789.

Thus the P-value in this analysis is 0.047.

Interpret results. Since the P-value (0.047) is less than the significance level (0.10), we have to reject the null hypothesis.

Reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that u < 370.