According to the Food Marketing Institute, the average weekly grocery expense in

Question

According to the Food Marketing Institute, the average weekly grocery expense in the United States in 2002 was exist36 per person. A random sample of 18 people yielded the following weekly expenses. Assume the population of weekly expenses is normally distributed. What is the point estimate for the population mean weekly grocery expense? What is the sample standard deviation? What is the standard error? Using the 0.05 level of significance, conduct a 5-part hypothesis test of the claim that the average weekly grocery expense is greater than exist36. Clearly label all parts of the hypothesis test. Use complete sentences in parts IV and V below. Specifically, show: I. the null and the alternative hypotheses: II. 1, the alpha level and the degrees of freedom (if appropriate), 2, . a graphic depiction with labels of the rejection and nonrejection regions, and 3, the decision rule: III. the test statistic: IV. your conclusion, reflecting the value of the test statistic, the critical bound of your decision rule, your conclusion and the confidence you have in that conclusion: V. implications from your hypothesis test. Construct the 95% confidence interval estimate of the mean. Clearly label the lower and upper bound.

Explanation / Answer

Solution:

23.

i. H0: mu=36 (average weekly grocery expense in United States in 2002 is $36)

H1:mu>36 (average weekly grocery expense in United states in 2002 is more than $36)

ii. 1. The alpha level:0.05; Critical t at df=17 [df=n-1, where n is the sample size] and alpha=0.05 is 1.74. 2. Rejection region is beyond 1.76. 3. Reject H0, if observed test statistic is higher than 1.74.

iii. Compute mean, xbar and standard deviation,s by using following formula.

xbar=sigmax/n, and s=sqrt[1/n-1sigma(x-xbar)^2], where n is sample size.

xbar=38, s=5.04

t=(xbar-mu)/(s/sqrt n)

=(38-36)/(5.04/sqrt 18)

=1.68

iv. The test statistic do not fall in critical region, therefore, fail to reject H0.

v. There is no sufficient sample evidence to conclude that average weekly grocery expense in United states in 2002 is more than $36.

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