A 08:55 31 Question 4 B 50 The pressure Y of a gas corresponding to various volumes X is recorded, and the data is tabulated below: Volume X(cm³) 40 50 60 80 90 5.6 A73 K/s Pressure Y(kg/cm) 54.7 41.2 32.6 15.6 9.5 a) Using the model x, ay, +b+, 1-12.5 find the least square estimate of a and band write the regression line x=ay+b. b) Determine the volume, if the pressure is 4.8kg/cm [10] 121 c) Compute and interpret the sample correlation coefficient r of the data. [8] Question 5 According to Mendelian genetic theory, the offspring of a certain cross of bearded iris plants should be coloured pink, blue or red with probabilities 9 3 16 16 and respectively. If an 16 experiment yields 68, 34 and 42 in each category, does the experiment support the Mendelian theory? Use the chi-square test at the 5% significant level to answer the following: [3] (a) Complete the table for the experiment yields and corresponding theoretical yields. (b) Formulate the null and attenutive hypothesis for the chi-square test. (c) Evaluate the test statistic of the chi-square model. [2] 14] (d) Find the critical value of test at 5% significant level. [3] (e) State clearly the decision rule of the test, show clearly the acceptance and critical regions of the mill hypothesis. [4] (f) Give a conclusion based on your computed test statistics, on whether the experiment support the Mendelian genetic theory. [4] 3 Question 6 Let X be a random variable with probability function given by f(x) = (x)~ x! -.0<0<1,x=1,2,3,4,5..... Find the expectation of X, u=E[X]. (ii) Hence find the expectation of Y=3-2X. Edit Annotate Fill & Sign Convert All ט 0 O כ 171 131 A 08:54 31 50 D. 1 981 73 B/s Question 1 (a) The concentration of a random sample of ten containers of hydrochloric acid are: 89,9.2, 8.7, 9.5, 10.3, 8.1,9.8, 10.2, 11.3,85,8.8, 10.0 Find the 95% confidence interval for mean concentration of containers, assuming the concentration of containers are normally distributed. (ii) If a container has a concentration of 8.3 does it belong to this sample? Reason. (iii) Find the sample size required for the margin of error to be less than 0.01. [8] [3] [4] (b) An environmental inspector conducts a study to investigate the prevalence of pollution along the river banks. A study shows that 250 out 1000 locations are contaminated. (i) Find the 95% confidence interval of the proportion of contamination. 151 (ii) Find the sample size a required for the margin of error to be less than 0.02. [5] Question 2 Let X-x, be sample mean and S² (X,-X)² sample variance of the random sample of size n=6, from N (30,12) population. (a) State the distribution of X and S. [5] (b) Compute (i) P(2.748

A 08:55 31 Question 4 B 50 The pressure Y of a gas corresponding to various volumes X is recorded, and the data is tabulated below: Volume X(cm³) 40 50 60 80 90 5.6 A73 K/s Pressure Y(kg/cm) 54.7 41.2 32.6 15.6 9.5 a) Using the model x, ay, +b+, 1-12.5 find the least square estimate of a and band write the regression line x=ay+b. b) Determine the volume, if the pressure is 4.8kg/cm [10] 121 c) Compute and interpret the sample correlation coefficient r of the data. [8] Question 5 According to Mendelian genetic theory, the offspring of a certain cross of bearded iris plants should be coloured pink, blue or red with probabilities 9 3 16 16 and respectively. If an 16 experiment yields 68, 34 and 42 in each category, does the experiment support the Mendelian theory? Use the chi-square test at the 5% significant level to answer the following: [3] (a) Complete the table for the experiment yields and corresponding theoretical yields. (b) Formulate the null and attenutive hypothesis for the chi-square test. (c) Evaluate the test statistic of the chi-square model. [2] 14] (d) Find the critical value of test at 5% significant level. [3] (e) State clearly the decision rule of the test, show clearly the acceptance and critical regions of the mill hypothesis. [4] (f) Give a conclusion based on your computed test statistics, on whether the experiment support the Mendelian genetic theory. [4] 3 Question 6 Let X be a random variable with probability function given by f(x) = (x)~ x! -.0<0<1,x=1,2,3,4,5..... Find the expectation of X, u=E[X]. (ii) Hence find the expectation of Y=3-2X. Edit Annotate Fill & Sign Convert All ט 0 O כ 171 131 A 08:54 31 50 D. 1 981 73 B/s Question 1 (a) The concentration of a random sample of ten containers of hydrochloric acid are: 89,9.2, 8.7, 9.5, 10.3, 8.1,9.8, 10.2, 11.3,85,8.8, 10.0 Find the 95% confidence interval for mean concentration of containers, assuming the concentration of containers are normally distributed. (ii) If a container has a concentration of 8.3 does it belong to this sample? Reason. (iii) Find the sample size required for the margin of error to be less than 0.01. [8] [3] [4] (b) An environmental inspector conducts a study to investigate the prevalence of pollution along the river banks. A study shows that 250 out 1000 locations are contaminated. (i) Find the 95% confidence interval of the proportion of contamination. 151 (ii) Find the sample size a required for the margin of error to be less than 0.02. [5] Question 2 Let X-x, be sample mean and S² (X,-X)² sample variance of the random sample of size n=6, from N (30,12) population. (a) State the distribution of X and S. [5] (b) Compute (i) P(2.748

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

See similar textbooks