Chapter 8 Class Activity

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Apr 3, 2024

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STAT 2103 – Chapter 8 Activity Description: Complete the following questions and submit your answers in Canvas. This assignment is worth 9 points. Problem 1 : A group of 112 companies in the insurance industry has a mean annual profit as percent of revenue of 5.4 with a standard deviation of 1.6 while the mean annual profit as a percent of revenue for a group of 100 health care companies was 4.6 with a standard deviation of 1.4. GIVEN N1=112 X1=5.4 S1=1.6 N2=100 X2=4.6 S2=1.4 a. Find a 90% confidence interval for the difference in mean annual profit. Round to 2 decimal places. sample size 112 100 Mean 5.4 4.6 SD 1.6 1.4 CL 0.9 LOS 0.1 DF 210 t-stat -1.652141981 SQRT 0.207612767 CI 0.456994231 1.143005769 (0.46,1.14) this confidence interval implies difference between both mean that lies between (0.46,1.14) with 90% confidence. b. At the 90% level of confidence, what can you conclude (i.e., does it appear that one industry group has a higher profit as a percentage of revenue)? We have sufficient proof that one industrial group has greater profits as a proportion of revenue because the interval is above zero. Problem 2 : In a group of 355 randomly selected high school females, 103 elected to take mathematics as an elective their senior year. In a group of 501 randomly selected high school males, 148 decided to take mathematics as an elective in their senior year. Is there evidence to suggest fewer females take math as an elective? Test at the α = .10 significance level. Submit the…
Given N1- 355 X1-103 N2- 501 X2- 148 C1 = 0.90 Alpha = 0.10 P1 = 103/355 = 0.290 P2 = 148/501= 0.295 Pooled = (103+148)/(355+501)= 0.293 SE= SQRT(0.293*(1-0.293)*((1/355)+(1/501))=0.032 a) Test statistic. Round to 2 decimal places. (0.290-0.295)/0.032= -0.17 b) P-value. Round to 3 decimal places. =NORM.DIST(-0.17,0,1, true)= 0.434 c) Conclusion. Since the P-Value is Greater than alpha, we fail to reject the null hypothesis, as there is insufficient evidence to conclude that fewer females take math as an elective
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