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1. Two suppliers manufacture a plastic gear used in a laser printer. The impact strength of these gears measures in foot-pounds is an important characteristic. A random sample of 10 gears from supplier 1 results in x1 = 290 and s1 = 12 while another random sample of 16 gears from the second supplier results in x2 = 321 and s2 = 22.

Is there evidence to support the claim that supplier 2 provides gears with higher mean impact strength. Use a =0.04, and assume that both populations are normally distributed with equal variances.

2. Amstat News (December 2004) lists median salaries for associate professors of statistics at research institutions and at liberal arts and other institutions in the United States. Assume a sample of 200 associate professors from research institutions having an average salary of $70,750 per year with a standard deviation of $6000. Assume also a sample of 200 associate professors from other types of institutions having an average salary of $65,200 with a standard deviation of $5000. Test the hypothesis that the mean salary for associate professors in research institutions is $2000 higher than for those in other institutions. Use a 0.05 level of significance.

Note: Follow the steps outlined in Test of Hypothesis (below image), which include your conclusion, and round the critical value as well as test statistic to four decimal places.

CLAIM: (state the claim of the problem) 1. Ho : H1 - H2 = 0 , (describe Ho) there's no significant difference H1 : H1 - Hz