A medical service company that makes insulin used by diabetics claim that a full

ID: 3155386 • Letter: A

Question

A medical service company that makes insulin used by diabetics claim that a fully charged battery in their pump lasts 90 hours. A consumer group is concerned that the battery life is lower. The consumer group takes a random sample of 34 pumps and finds an average batery life of 88.1 hours with a standard deviation of 3.6 hours

1. Write appropriate hypotheses if the consumber group wishes to refute the company's claim:

2. Assuming any necessary conditions are met, what test will you use to test your hypothesis? Give the name of the test or formula:

3. Test your hypothesis at the 2% level of significance. You are to assume any necessary conditions have met (dont check them). Draw and lable a picture. Give the test statistic and p-value.

4. State your ocnclusion in the context of the problem.

5. Carefully explain what the p-value means

6. Explain the consequences of a type two error in this situation.

Explanation / Answer

A medical service company that makes insulin used by diabetics claim that a fully charged battery in their pump lasts 90 hours. A consumer group is concerned that the battery life is lower. The consumer group takes a random sample of 34 pumps and finds an average battery life of 88.1 hours with a standard deviation of 3.6 hours

Solution:

We are given

Sample mean = 88.1

Sample standard deviation = 3.6

Sample size = 34

Population mean = 90

Level of significance = alpha = 0.02 or 2%

Answer 1

The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: A fully charged battery in the pump lasts 90 hours.

Alternative hypothesis: Ha: A fully charged battery in the pump do not lasts 90 hours.

H0: µ = 90 versus Ha: µ 90

Answer 2

Here, we have to use the one sample t test for the population mean for checking the given claim.

Answer 3

The formula for test statistic t value is given as below:

Test statistic = t = (sample mean – population mean) / [sample standard deviation / sqrt(n)]

Where n is the sample size.

We are given

Sample mean = 88.1

Sample standard deviation = 3.6

Sample size = 34

Population mean = 90

Level of significance = alpha = 0.02 or 2%

By plugging all values in the formula we get the following results

t Test for Hypothesis of the Mean

Data

Null Hypothesis m=

Level of Significance

0.02

Sample Size

Sample Mean

88.1

Sample Standard Deviation

3.6

Intermediate Calculations

Standard Error of the Mean

0.6174

Degrees of Freedom

t Test Statistic

-3.0774

Two-Tail Test

Lower Critical Value

-2.4448

Upper Critical Value

2.4448

p-Value

0.0042

Reject the null hypothesis

Answer 4

Here, we get the p-value as 0.0042 which is less than the given level of significance or alpha value 0.02, so we reject the null hypothesis that a fully charged battery in the pump lasts 90 hours. This means we concluded that a fully charged battery in the pump do not lasts 90 hours.

Answer 5

The p-value means the probability of the finding the observed, or more extreme, results when the null hypothesis (H 0) of a study question is true.

Answer 6

Type II error in this situation is defined as the probability of do not rejecting the null hypothesis that a fully charged battery in the pump lasts 90 hours however the fully charged battery in the pump do not lasts 90 hours.