1 The Highway Safety Department wants to study the driving h

1. The Highway Safety Department wants to study the driving habits of individuals. A sample of 121 cars traveling on the highway revealed an average speed of 60 miles per hour with a standard deviation of 11 miles per hour. Determine a 95% confidence interval estimate for the speed of all cars.

2. In the past, the average age of employees of a large corporation has been 40 years. Recently, the company has been hiring older individuals. In order to determine whether there has been an increase in the average age of all the employees, a sample of 64 employees was selected. The average age in the sample was 45 years with a standard deviation of 16 years. Let a = .05. Draw and label the distribution and identify the reject region(s).

a.

State the null and the alternative hypotheses.

b.

Compute the test statistic.

c.

Using the critical value approach, test to determine whether or not the mean age of all employees is significantly more than 40 years and state your conclusion.

3. A lathe is set to cut bars of steel into lengths of 6 centimeters. The lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 6 centimeters. A sample of 121 bars is selected randomly and measured. It is determined that the average length of the bars in the sample is 6.08 centimeters with a standard deviation of 0.44 centimeters. Draw and label the distribution and identify the reject region.

a.

Formulate the hypotheses to determine whether or not the lathe is in perfect adjustment.

b.

Compute the test statistic.

c.

Using the critical value approach, what is your conclusion? Let a = .05.

Solution

1)sample mean = 60 , sample s.d = 11 , n =121

t-score for 95% confidence = 1.97993..

so, confidence interval = [ 60 - ( 1.97993 * 11 / sqrt(121) ) , 60 + ( 1.97993 * 11 / sqrt(121) ) ]

= [ 58.02007 , 61.97993 ].......


2) H0 : average population age = 40 ag. H1: average population age > 40....

sample mean = 45...and sample s.d =16.. n = 64..

test statistic = (45 -40 ) / ( 16 / sqrt ( 64) ) = 2.5...
critical value for a = .05 and df = 63 is 1.669402...

test statistic is > critical value.....so, we have to reject H0 and state that indeed there has been anincrease in the average age of all the employees...

3) populaton mean = 6

sample mean = 6.08 and sample s.d = 0.44......n =121

H0: population mean of bars = 6 ag. H1 : not equal to 6..
critical value = + or - 1.97993...distributin is T-distribution and rejection region is:
reject H0 if | test statistic | > | 1.97993| i.e, reject H0 if test statistic > 1.97993 or, -test statistic < -1.97993

Test statistic = ( 6.08 - 6 ) / ( 0.44 / sqrt ( 121) ) = 2...

so, test statistic is > critical value , so we have to rejcet H0 and claim that the average of the bars is not equal to 6 cm i.e, the lathe is not in perfect adjustment.