Final Exam Ec315

PART I. HYPOTHESIS TESTING
PROBLEM 1 A certain brand of fluorescent light tube was advertised as having an effective life span before burning out of 4000 hours. A random sample of 84 bulbs was burned out with a mean illumination life span of 1870 hours and with a sample standard deviation of 90 hours. Construct a 95 confidence interval based on this sample and be sure to

interpret this interval.

Answer
Since population standard deviation is unknown, t distribution can be used construct the confidence interval. 

The 95% confidence interval is given by  X  t / 2,n 1



S
S
, X  t /2,n 1

n n Details
Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation
Sample Mean
Sample Size
Confidence Level

90
1870
84
95%

Intermediate Calculations
Standard Error of the Mean
9.819805061
Degrees of Freedom
83
t Value
1.988959743
Interval Half Width
19.53119695
Confidence Interval
Interval Lower Limit
1850.47
Interval Upper Limit
1889.53

2
PROBLEM 2 Given the following data from two independent data sets, conduct a one -tail hypothesis test to determine if the means are statistically equal using alpha=0.05. Do NOT do a confidence interval. n1 = 35 n2 = 30 xbar1= 32 xbar2 = 25 s1=7 s2 = 6
Answer
H0:µ1=µ2
H1: µ1>µ2
Test statistics used is t 

X1  X 2
S

2
(n1  1) S12  (n2  1) S2 n1n2 ~ tn1  n1 2 where S  n1  n2  2 n1  n2

Decision rule : Reject the null hypothesis, if the calculated value of test statistic is greater than the critical value.
Details
t Test for Differences in Two Means
Data
Hypothesized Difference
Level of Significance
Population 1 Sample
Sample Size
Sample Mean
Sample Standard Deviation
Population 2 Sample
Sample Size
Sample Mean
Sample Standard Deviation

0
0.05
35
32
7
30
25
6

Intermediate Calculations
Population 1 Sample Degrees of Freedom
34
Population 2 Sample Degrees of Freedom
29
Total Degrees of Freedom