Probability And Statistics In Engineering And Science

1. An employment information service claims the mean annual salary ar a homecare physical therapist is more than $30,000. The annual salaries (in dollars) for a random sample of 12 homecare physical therapists are shown in the below. At a: = 0.10, is there enough evidence to support the claim that the mean salary is more than $30,000?I Assume that the data is independent and normally distributed B9245, 86013, 83151, 69?? 1, STE-l4, 6T964, T6523, 90268, 90440, 93538, T6999, 6825'? a) {4 points) Write the claim mathematically and identify the null and alternative hypothesis. Identify which is the claim. b] {3 points) Explain why using the ttest was necessary in this situation. c) {6 points) Paste your command[s] and output from E into your solutions le. d] {3 points) Decide whether to reject or fail to reject the null hypothesis based on the Pyalue- Explain your reasoning. e) {3 points) Interpret the decision in the context of the original claim. 2. In a study, 760 men with recurrent prostate cancer underwent radiation with or without a type of hormone-based chemotherapy. For 24 months, 384 subjects were given the chemotherapy and 376 subjects were given placebo. The numbers who survived and did not survive after 12 years were tracked. The results are shown below. At a = 0.01, can you support the claim that the proportion of 12-year survivors is greater for subjects who were given the chemotherapy than the subjects who were given placebo? (Adapted from the New England Journal of Medicine) How Many Subjects Survived After 12 Years and How Many Did Not? Did not survive 91 108 Survived Survived 293 268 Chemotherapy Placebo a) (4 points) Write the claim mathematically and identify the null and alternative hypothesis. Identify which is the claim. b) (3 points) Explain why using the z-test can be used in this situation. c) (6 points) Paste your command(s) and output from R into your solutions file. d) (3 points) Decide whether to reject or fail to reject the null hypothesis based on the P- value. Explain your reasoning. e) (3 points) Interpret the decision in the context of the original claim.3. Fusible interlinings are being used with increasing frequency to support outer fabrics and improve the shape and drape of various pieces of clothing. The article uCompatibility of Outer and Fusible Interlining Fabrics in Tailored Garments" (Tactile Res. J: 1992: 132142) gave the accompanying data on extensibility (3/6) at l gmfom for both highquality fabric (H) and poorquality fabric {P} specimens: H: 1.2, til-9, -T, 1-1], 1.2, 1.2, 1-1, 0-9, 1-2, 1-9, 1.3, 2.1, 1.6, 1-3, 1-4, 1.3, 1.9,1-6, {1.3, 2-0, l-T, 1:5, 2.3, 2-0 P:1.~, 1.5, 1.1, 2-1, 15,1-3, 1:1], 2.5 Assume that the data is normally distributed and assume that the population standard deviations are equal Use the twosample ttest to decide whether true average extensibility differs for the two types of fabrics at or = [1.135. a) {3 points) Write the claim mathematically and identify the null and alternative hypothesis. Identify which is the claim. b) {3 points) Explain why using the ttest was necessary in this situation- c) {3 points) Explain whether you should use the 'Pool variances= option or not. Why or why not? d) {I5 points) Paste your command[s] and output from E into your solutions le. e) {3 points) Decide whether to reject or fail to reject the null hypothesis based on the P value. Explain your reasoning. {3 points) Interrupt the decision in the context ofthe original claim. 4. Fusihle interlinings are being used with increasing frequency to support outer fabrics and improve the shape and drape of various pieces of clothing. The article \"Compatibility of lDuster and Fusible Interlining Fabrics in Tailored Garments\" (Tactile Res. J: 199?: 1371142) gave the accompanying data on extensibility (321:) at 11111 gmtcm for both highquality fabric (H) and poorquality fabric {P} specimens: H: 1.2, 0-9, {II-Tu", 1.11, 1.1', 1.'Ir', 1.1, (1.9, 1-7", 1.9, 1.3, 2.1, 1.6,1-3, 1-4, 1.3, 1.11.6, {1.3, 2-11, 1-7:", 1.5, 2.3, 2-1} P2135, 1.5, 1.1, 2-1, 1-5, 1-3, 1.11], 2.5 Assume that the data is normally distributed and assume that the population standard deviations are not equal. Use the twosample ttest to decide whether true average extensibility differs for the two types of fabrics at o: = [1.115. a) {4 points) Write the claim mathematically and identify the null and alternative hypothesis. Identify which is the claim. b) {3 points) Explain why using the ttest was necessary in this situation- c) {3 points) Explain whether you should use the 'Pool variances= option or not. Why or why not? d) {E points) Paste your command[s] and output from E into your solutions le. e) {3 points) Decide whether to reject or fail to reject the null hypothesis based on the Pvalue- Explain your reasoning. f) {3 points) [ntermt the decision in the context of the original claim. 5. Use R and the data in Questions #3 and #4 to: a) (6 points) Compute the standard deviation for both data sets. b) (7 points) Provide a boxplot as demonstrated in the lecture videos in Section 8.2. c) (7 points) Based on the boxplot and the sample standard deviations, which analysis is more appropriate for that data? Is it the analysis in Question #3 or the analysis in Question #4? Why