Test whether the sample evidence indicates that the average time an employee stays with a

1. Test whether the sample evidence indicates that the average time an employee stays with a company in their current positions is less than 3 years when a random sample of 64 employees yielded 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 20 observations.

    = -3.5- (1.5)X
R²= 0.85 and s_b1 = 0.70
Interpret regression results and the value of the coefficient of Determination. Predict the value of Y when X is equal to 10. Calculate the correlation coefficient between Y and X. Test to determine 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 of heating time (hours). Results based on 20 metal sheets are given below. Use the simple linear regression model.
∑X = 40
∑X² = 200
 ∑Y = 80
 ∑Y² = 1120
 ∑XY = 460

Find the estimated y intercept and slope and write the equation of the least squares regression line. Estimate Y when X is equal to 3 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation.

Multiple Choice

4.  If a one-sided null hypothesis is rejected for a single mean at a given significance level, the corresponding two-sided null hypothesis (i.e., the same sample size, the same standard deviation and the same mean) will _________ be rejected at the same significance level. 
A. Always
B. Sometimes
C. Never

5.  If a null hypothesis is rejected at a significance level of 0.05, it will ______ be rejected at a significance level of 0.10 
A. Always
B. Sometimes
C. Never