EXAMPLE 1 with a standard deviation of $7,000 for a sample of 35 households. At the.01 significance level can we conclude the mean income in Bradford is more? Two cities, Bradford and Kane are separated only by the Conewango River. There is competition between the two cities. The local paper recently reported that the mean household income in Bradford is $38,000 with a standard deviation of $6,000 for a sample of 40 households. The same article reported the mean income in Kane is $35,000

Example 1 continued Step 2 State the level of significance. The.01 significance level is stated in the problem. Step 3 Find the appropriate test statistic. Because both samples are more than 30, we can use z as the test statistic. Step 1 State the null and alternate hypotheses. H 0 : µB < µK H 1 : µB > µK Step 4 State the decision rule. The null hypothesis is rejected if z is greater than 2.33 or p <.01.

Example 1 continued Step 5: Compute the value of z and make a decision. The p(z > 1.98) is.0239 for a one-tailed test of significance. Because the computed Z of 1.98  of.01, the decision is to not reject the null hypothesis. We cannot conclude that the mean household income in Bradford is larger.

Example 3 A recent EPA study compared the average of stock prices of domestic and foreign companies. A sample of 15 domestic stock prices a mean of 33.7 $ per share with a standard deviation of 2.4 $. A sample of 12 foreign stock prices revealed a mean of 35.7 $ per share with a standard deviation of 3.9. At the.01 significance level can the EPA conclude that the average stock prices is higher foreign companies?

Example 3 continued Step 1 State the null and alternate hypotheses. H 0 : µ D > µ F H 1 : µ D < µ F Step 2 State the level of significance. The.01 significance level is stated in the problem. Step 3 Find the appropriate test statistic. Both samples are less than 30, so we use the t distribution.

Example 3 continued Step 4 The decision rule is to reject H 0 if t< There are n- 1 or 25 degrees of freedom. Step 5 We compute the pooled variance.

Example 3 continued We compute the value of t as follows.

You are given the following table of stock prices for Toshiba and Sony in USD. Assume that both companies are operating independently from each other. Answer the following questions,Run Hypothesis Testing to check if Sony average stock prices are significantly different from Toshiba average stock prices or not? Explain your results following all the steps.(hint: H0 µs=µT ; H1 µs≠µT) DATESSonyToshiba $19$ $14$ $15$ $16$ $18$ $19$ $20$ $30$ $10