The Linear Correlation Coefficient

Problem 1 A study claims that 70% of children under the age of 13 in British Columbia have been vaccinated from the chicken pox. A survey of randomly selected residents of a certain city included 650 children who were under the age of 13, and 204 of them were not vaccinated. Part a What is the approximated probability that sample proportion of non-vaccinated children in a sample of 650 children is more than 204/650? (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest four decimal places). Answer =��(650! 0!(6500!)0.70(10.7)6500)+ +(650! 204!(650204!)0.7204(10.7)650204) =��(��)=0.3138(10.3138) 650=0.0182 Pr(��0.313846154 0.01820.31460.313846154 0.0182) Pr(�0.04) ����=0.4831 Part b Is the number of non-vaccinated children in this city sample unusually high, low, or neither? Answer: The number is neither high nor low, its in the middle. Problem 2. (2 points) IMPORTANT: The answer you submit here is worth 2 marks. The corresponding work you upload into UR Courses will be worth an additional 12 marks. Be sure to interpret your answer in your written work. The standard deviation of the length of skateboards in a board shop is 0.98 in. A random sample of 27 skateboards is selected and found to have a mean length of 30.5 in. Find a 95% confidence interval for the true mean length of skateboards in the board shop. Your results should be accurate to the nearest hundredth cm (at least). Answer 95%����=30.52.0560.98 27 95%����[30.11,30.89] We are 95% confident that the true population average for skateboard length lies somewhere between 30.11 and 30.89. Proble m 3. (1 point) IM PORTANT: The answer you submit here is worth 1 mark. The corresponding work you upload into UR Courses will be worth an additiona l 7 marks. Be sure to interpret your answer in your written work. Consider the following small data set. Subject x y 11 55 2020 22 1515 2929 33 1111 1919 44 1616 1616 55 1111 2020 Find the linear correlatio n coeffic ie nt. Give your answer correct to four decimal places. You may use the following facts: �=58,�=104,�2=748,�2=2258,��=1220x=58,y=104,x2=748,y2=2258,xy=1220. ��=r= 5122058104 (5748582)(522581042) =0.1611 Question 4 Proportion is, =0.58 �=0.580.54 0.54(10.54) 990 =2.525 ���������=10.99430 ��=0.0057 The p-value is 0.0057, a value less than 5% level of significance and therefore, we conclude that the sample proportion was significantly higher than the hypothesized proportion. Problem 5 ���=(����)2= �=57+82+93+46+40 5=318 20=15.9 ���=(����)2=(915.9)2++(915.9)2=673.8 ���=145.5 ���=������=673.8145.5=528.3 ����=528.3 4=132.075 ����=145.5 15=9.7 �=���� ����=132.075 9.7=13.61598 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 528.3 4 132.075 13.61598 7E-05 3.055568 Within Groups 145.5 15 9.7 Total 673.8 19 Problem 6 The contents of 31 cans of Coke have a mean of 12.15 fl oz and a standard deviation of 0.1 fl oz. Find the value of the test stat****ic, correct to two decimal places, used to test the claim that the population mean content is 12 fl oz. Solution �=12.512 0.1 31 =27.84