Statistics- Test whether the sample evidence indicates that the average

QUESTION

1. Test whether the sample evidence indicates that the average time an employee stays with acompany in their current positions is less than 3 years when a random sample of 64 employeesyielded a mean of 2.76 years and s = 0.8. Use = 0.01. Assume normal distribution.2. Use the following results obtained from a simple linear regression analysis with 20observations.^Y= -3.5- (1.5)XR2= 0.85 and sb1 = 0.70Interpret regression results and the value of the coefficient of Determination. Predict the value ofY when X is equal to 10. Calculate the correlation coefficient between Y and X. Test todetermine if there is a significant relationship between the independent and dependent variable at= 0.05 and 0.01. Perform a two-tailed test.3. An experiment was performed on a certain metal to determine if the strength is a function ofheating time (hours). Results based on 20 metal sheets are given below. Use the simple linearregression model.∑X = 40∑X2 = 200∑Y = 80∑Y2 = 1120∑XY = 460Find the estimated y intercept and slope and write the equation of the least squares regressionline. Estimate Y when X is equal to 3 hours. Also determine the standard error, the Mean SquareError, the coefficient of determination and the coefficient of correlation.Multiple Choice4. If a one-sided null hypothesis is rejected for a single mean at a given significance level, thecorresponding two-sided null hypothesis (i.e., the same sample size, the same standard deviationand the same mean) will _________ be rejected at the same significance level.A. AlwaysB. SometimesC. Never5. If a null hypothesis is rejected at a significance level of 0.05, it will ______ be rejected at asignificance level of 0.10A. AlwaysB. SometimesC. Never1

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