Question

The National Retail Federation reported that Halloween spending for 2009 had declined from previous years. According to their polls, the average adult spent approximately $66 on Halloween costumes, candy, decorations, etc. in 2008. However, a sample of n= 30 families in 2009 produced a mean of M = $56 with SS = 11600. Use the steps below to determine whether these data indicate a significant decrease in 2009 holiday spending compared to 2008. a. Which type of hypothesis test is needed: one-sample z or one-sample t? b. State the null and alternative hypotheses using the appropriate symbols. Be sure to consider whether this is a one-tailed test or a two-tailed test. c. Using an alpha level of 0.05 identify the critical value that will serve as the decision criterion. d. Compute the appropriate test statistic. Show all formulas that you use as well as your work and circle your calculated test statistic. e. State your decision regarding the null hypothesis -Reject or Fail to Reject. f. If appropriate, compute effect size (include formula!). Otherwise state N/A g. Give a plain English interpretation of your conclusion that includes the relevant statistics and is presented in APA format.

Answer 1

a) one-sample t

b) $H_{0}: \mu \geq 66$

   $H_{1}: \mu < 66$

This is a one-tailed test.

c) df = 30 - 1 = 29

At alpha = 0.05, the critical value is t_0.05,29 = -1.699

d)

$s = \sqrt{\frac{SS}{n - 1}}$

    $= \sqrt{\frac{11600}{30 - 1}}$

    = 20

The test statistic is

$t = \frac{M- \mu}{s/\sqrt n}$

$= \frac{56 - 66}{20/\sqrt {30}}$

= -2.74

e) Since the test statistic value is less than the critical value(-2.74 < -1.699), so we should reject H₀.

f) Effect size is

$d = \frac{M - \mu}{s}$

    $= \frac{56 - 66}{20}$

   

g) At 0.05 significance level, there is sufficient evidence to conclude that there is a significant decrease in 2009 holiday spending compared to 2008.