PLEASE HELP TO SOLVE THIS QUESTION DEAR TUTOR. AND PLEASE DONT COPY FROM OTHER WEBSITE SUCH AS CHEGG AND ETC. GIVE AN SUPER EXPLAINATION'S
Key Formula Mean[Population) Mean(Sample) Mean Grouped Data Mean Grouped Data 2x 2 x Population Sample) N EMf EMf H = total f total f Variance (Population) Variance (Sample) Variance Grouped Data Variance Grouped Data Z(x - 4)- Z(x -7): (Population) (Sample) O' = $2 : N n - 1 X(M - H)=f E(M - )f total f total f - 1 Standard deviation Standard deviation (Sample) Standard deviation Grouped Standard deviation (Population) Data (Population) Grouped Data (Sample) E(x - X)2 [(x - 1) D = n- 1 E(M - 4)2f X(M - D)If D = S = N total f total f - 1 Standard normal value Standard error of mean single mean (known o) Single proportion X - ! X - H Z = - OX = P - P pq Two means independent Single mean (unknown o) Two means independent Dependent samples samples (known o) and oz) x - P samples (unknown o) and 02) t = - d t = Vn t= of n2 92 - [1 - 1)67 + (72 - 1)65 Ed- d)' M +2 -2 n - 1 df= n + n-2 d : Ed df=n-1 Coefficient of Correlation Test for significant Linear Regression Equation Slope for Regression line Z(x - D)( V - D) correlation Y=a+bX R= = b = R- (n - 1)(5,) (5,) 1 = 1 - R2 17 - Intercept for Regression line a = V-bxAnswer all questions and show your calculations for every question. Question 1 The data shows the world most famous Football players' salary (in millions of US$) for a specific year. Answer the following questions based on the data. 77 84 91 92 93 94 94 97 98 98 98 99 99 100 100 100 102 102 102 103 103 104 105 106 106 107 107 109 109 110 118 123 i. Construct a frequency distribution. (3 Marks) ii. Using the result from part (i), calculate the relative frequencies for each class. (1 Marks) ili. Using the result from part (i), calculate the cumulative frequencies for each class. (1 Marks) iv. Construct a frequency histogram for these data. (3 Marks) V. Using the result from part (i), compute the mean. (2 Marks) vi. Using the result from part (v), compute the standard deviation. (5 Marks) (Total: 15 Maks)Question 2 a. An advertising company plans to market a product to low-income families. A study states that for a particular area, the mean income per family is $24,596 and the standard deviation is $6,256. Assume the variable is normally distributed. Find the probability that a randomly selected family whose income is; F Less than $20,000. (3 Marks) ii. Between $20,000 and $30,000. (3 Marks) ii. If the company plans to target the bottom 18% of the families based on income, find the cutoff income. (3 Marks) b. Noise levels at various area urban hospitals were measured in decibels. The mean of the noise levels in 84 randomly selected corridors was 61.2 decibels, and the standard deviation of the population was 7.9. At 95% confidence level, what is the margin error? (2 Marks) Construct the 95% confidence interval for the population mean. (3 Marks) Ill. If a person claimed that the noise level at a urban hospital is 58 decibel, would the claim be believable? (1 Mark) (Total: 15 Marks)Question 3 a. A research reported that undergraduate students have a mean credit card balance of $3,173. This figure was an all-time high and had increased 44% over the previous five years. Assume that a current study is being conducted to determine if it can be concluded that the mean credit card balance for undergraduate students has continued to increase compared to the report. A sample of 180 undergraduate students showed a mean credit card balance of $3,325 and the population standard deviation is $1,000. Use 5% significance level to test the claim that undergraduate students have a mean credit card balance more than $3, 173. Identify the claim and state the Ho and Hi. (1 Mark) li. Find the critical value. (1 Mark) i. Calculate the test statistic. (2 Marks) v. Make a decision to reject or fail to reject the Ho. (1 Mark) V. Interpret the decision in the context of the original claim. (1 Mark) b. A shareholders' group, in lodging a protest, claimed that the mean tenure for a chief executive officer (CEO) was at least nine years. A survey of companies reported in The Wall Street Journal found a sample of 25 companies revealed a mean tenure of 7.27 years for CEOs with a sample standard deviation of s = 6.38 years. Use 1% significance level to test the claim that the mean tenure for a chief executive officer (CEO) was at least nine years. Identify the claim and state the Ho and Hi. (1 Mark) i. Find the critical value. (1 Mark) ii. Calculate the test statistic. (2 Marks iv. Make a decision to reject or fail to reject the Ho. (1 Mark) V. Interpret the decision in the context of the original claim. (1 Mark) C. A study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands. To investigate whether this result applies to its own product, the manufacturer of a national name-brand ketchup asked a sample of shoppers whether they believed that supermarket ketchup was as good as the national brand ketchup. A sample of 100 shoppers showed 52 stating that the supermarket brand was as good as the national brand. Use 5% significance level to test the claim that the supermarket brand was as good as the national brand. 1. Identify the claim and state the Ho and H1. (1 Mark) i. Find the critical value. (1 Mark) II. Calculate the test statistic. (2 Marks v. Calculate the p-value for the test. (2 Marks) v. Make a decision to reject or fail to reject the Ho. (1 Mark) vi. Interpret the decision in the context of the original claim. (1 Mark) (Total: 20 Marks)Question 4 A researcher wanted to know the relationship between the price (in RM) of travelling suitcase with rollers and its' scores (higher scores indicate better overall test result). The following table shows the output of statistical analysis for the price and scores of travelling suitcase with rollers. Model Summary Adjusted R Std. Error of the Model R R Square Square Estimate 1 0.898 0.807 0.783 79.059 a. Predictors: (Constant), Scores Coefficients Unstandardized Standardized Coefficients Coefficients Model B Std. Error Beta P-value Constant) -696.668 168.088 4.145 0.003 Scores 14.293 2.473 0.898 5.778 0.001 a. Dependent Vanable: Price Comment on coefficient of correlation between Price and Scores. (1 Mark) Determine the coefficient of determination and explain this value in relation to the problem. (2 Marks) ii. At the 0.05 significance level is it reasonable to conclude that there is a significant relationship in the population between Price and Scores (2 Marks) iv. What is the value of Y-intercept? Interpret the meaning of the Y- intercept, a for this problem. (1 Mark) V. What is the value of the slope? Interpret the meaning of the slope, b for this problem. (1 Mark) vi. Write the regression equation for this problem from the output. (1 Mark) vii. Predict the Price if the Scores is 85. (2 Marks) (Total: 10 Marks)
