Question

1. Before they can be marketed, all new medical devices must be approved by the Food and Drug Administration (FDA). A new device has a protective cover which needs to be removed easily. A similar device, already on the market, has a cover that requires an average force of 8 pounds to remove. The laboratory test data on a random sample of 9 of the new device indicates the following removal forces:
   
       6.3, 8.4, 7.8, 6.4, 5.4, 8.0, 7.0, 6.2, 7.5
   
   Assume that the removal force has a normal distribution with a standard deviation σ =1.2 pounds. Does the data support the conclusion that the new device requires an average removal force less than 8 pounds? When making decision, let the probability of making a type I error be no more than 0.10.
   
   The correct set of null & alternative hypotheses are:

   	a.	Ho: μ > 8     Ha: μ ≤ 8
   	b.	Ho: μ < 8     Ha: μ ≥ 8
   	c.	Ho: μ ≤ 8     Ha: μ = 8
   	d.	Ho: μ ≥ 8     Ha: μ < 8

3 points   

QUESTION 9

1. The significance level of the test is:

   	a.	0.01
   	b.	0.02
   	c.	0.05
   	d.	0.10

2 points   

QUESTION 10

1. The test-statistic appropriate for this test is distributed as a

   	a.	Z random variable.
   	b.	t random variable.
   	c.	Z random variable, but can be approximated as a t.
   	d.	t random variable, but can be approximated as a Z.

3 points   

QUESTION 11

1. The computed value of test statistic equals

   	a.	-2.5
   	b.	-3.0
   	c.	2.3
   	d.	1.80

3 points   

QUESTION 12

1. The critical value of the test is:

   	a.	-2.326
   	b.	-2.576
   	c.	1.645
   	d.	-1.282

2 points   

QUESTION 13

1. The decision is that

   	a.	the alternative hypothesis is rejected. The average removal force is greater than 8 lbs.
   	b.	the null hypothesis is rejected. The average removal force is less than 8 lbs.
   	c.	Not enough information is given to answer this question.
   	d.	the alternative hypothesis is accepted. The average removal force is greater than 8 lbs.

3 points   

QUESTION 14

1. The p-value of the test is:

   	a.	0.0359
   	b.	0.0107
   	c.	0.0013
   	d.	0.0062

3 points   

QUESTION 15

1. Using p-value criterion, the decision is:

   	a.	Reject H0.
   	b.	Fail to reject H0.
   	c.	Reject Ha.
   	d.	Fail to reject Ha.

Answer 1

Solution:

Given:

Claim: the new device requires an average removal force less than 8 pounds

the removal force has a normal distribution with a standard deviation σ =1.2 pounds.

Sample size = n = 9

Sample:     6.3, 8.4, 7.8, 6.4, 5.4, 8.0, 7.0, 6.2, 7.5

Sample mean:

Question 8) The correct set of null & alternative hypotheses are:

d. Ho: μ ≥ 8     Ha: μ < 8

QUESTION 9) The significance level of the test is

d. 0.10

QUESTION 10 The test-statistic appropriate for this test is distributed as a

a. Z random variable

QUESTION 11 The computed value of test statistic equals

a. -2.5

QUESTION 12 The critical value of the test is:

Since Ha is < type, this is left tailed test.

The significance level = 0.10

Thus look in z table for Area= 0.1000 or its closest area and find z value.

Area 0.1003 is closest to 0.1000 and it corresponds to -1.2 and 0.08

Thus z = -1.28

thus correct answer is:

d. -1.282

QUESTION 13 The decision is that:

Since z test statistic = < z critical value = -1.282, we reject null hypothesis.

thus correct answer is:

b. the null hypothesis is rejected. The average removal force is less than 8 lbs.

QUESTION 14 The p-value of the test is:

For left tailed test , p-value is:

p-value = P(Z < z test statistic)

p-value = P(Z < -2.50)

Look in z table for z = -2.5 and 0.00 and find corresponding area.

P( Z< -2.50) = 0.0062

thus

p-value = P(Z < -2.50)

p-value =0.0062

thus correct answer is:

d. 0.0062

QUESTION 15 Using p-value criterion, the decision is:

Decision Rule:
Reject null hypothesis H0, if P-value < 0.10 level of significance, otherwise we fail to reject H0

Since p-value =0.0062 < 0.10 level of significance,we reject null hypothesis H0.

thus correct answer is:

a. Reject H0