Question

When doing a test, steps to be covered:

1. state the hypothesis and identify the claim
2. find the critical value from the table
3. compute the test value

make the decision to reject or not the null hypothesis

1) A company claims that cancer patients using drug X will live at least 8 more years.

n=16                                    

= 7.8 year

s = 2.4 year

a) Test at a=.05

b) Give the CIE at 90%           

1 B) A company creates  Bandana. A random sample of 25 turbines is taken and the sample mean life is 20.00 years with a standard deviation of 2.50 years. If you were constructing a 95% two-sided confidence interval estimate, the upper limit would be:

1 C))The Sonitra Coal  Company claims that there is less than 1 ppm (parts per million) of benzene in their water.

Data:

n=25

= 1.5 ppm    

s = .60 ppm

a) Test at a=.01

b) Give the CIE at 95%           

Answer 1

1)A) a) H₀: > 8

H₁: < 8

At alpha = 0.05, the critical value is t_{0.05, 15} = -1.753

The test statistic t = ()/(s/)

= (7.8 - 8)/(2.4/)

= -0.33

Since the test statistic value is not less than the critical value (-0.33 > -1.753), so we should not reject the null hypothesis.

b) At 90% confidence interval the critical value is t^* = 1.753

The 90% confidence interval is

+/- t^* * s/

= 7.8 +/- 1.753 * 2.4/

= 7.8 +/- 1.0518

= 6.7482, 8.8518

1)B) At 95% confidence interval the critical value is t^* = 2.064

The 95% confidence interval is

+/- t^* * s/

= 20 +/- 2.064 * 2.5/

= 20 +/- 1.032

= 18.968, 21.032

1)C) H₀: > 1

H₁: < 1

a) At alpha = 0.01, the critical value is t_{0.01, 24} = -2.492

The test statistic t = ()/(s/)

= (1.5 - 1)/(0.6/)

= 4.17

Since the test statistic value is not less than the critical value, so we should not reject the null hypothesis.

b) At 95% confidence interval the critical value is t^* = 2.064

The 95% confidence interval is

+/- t^* * s/

= 1.5 +/- 2.064 * 0.6/

= 1.5 +/- 0.25

= 1.25, 1.75