One measure of the value of a stock is its price to earningsratio (or P/E ratio). It is the ratio of the price of a stock pershare to the earnings per share and can be thought of as the pricean investor is willing to pay for $1 of earnings in a company. Astock analyst wants to know whether the P/E ratios for threeindustry categories differ significantly. The following datarepresent simple random samples of companies from three categories:(1) financial, (2) food, and (3) leisure goods.

Financial	Food	Leisure Goods
8.83	19.75	14.1
12.75	17.87	10.12
13.48	15.18	15.57
14.42	22.84	13.48
10.06	15.6	11.27

1. Test the null hypothesis that the mean P/E ratio for eachcategory is the same at the alpha = 0.05 level of significance withthe following steps:

• Formulate the null hypothesis and alternative hypothesis.

H₀: ______________________________ versus  H₁: _________________________________________.

• Check the assumptions and find MST, MSE, and the test statisticof fo with degrees of freedom of numerator and denominator.
• Make a decision and draw a conclusion with alpha = 0.05 levelof significance.

2. If the null hypothesis is rejected in part (a), use Tukey’stest to determine which pairwise means differ using a familywiseerror rate of alpha = 0.05, where qa,v,k = q0.05,12,3 = 3.773 fromthe table of critical values for Tukey’s Test.

H₀: __________________ versus  H₁: ____________________.

q0=

Decision:

H₀: __________________ versus  H₁: ____________________.

q0=    

Decision:

H₀: __________________ versus  H₁: ____________________.

q0=

Decision:

• Use lines to indicate which population means are notsignificantly different.