Statistics



Statistics

Chapter Nine

Problem 1)

H0: p = 0.001

H1: p < 0.001

Problem 2)

Ho: u(is) >= 18.4

Ha: u(is) < 18.4

Problem 3)

You need the test statistic to find the p-value. If you get a p-value that is less than the level of significance of 0.05, then that will tell you to reject the null hypothesis.

Problem 4)

2.5% on the either side of the normal curve.

Problem 5)

Type I error

Rejecting the null hypothesis when it is true

Example

A clinical trial is carried out to compare a new medical treatment with a old one. The statistical analysis shows a statistically significant difference in lifespan when using the new treatment compared to the old one. But the increase in lifespan is at most three days, with average increase less than 24 hours, and with poor quality of life during the period of extended life. Most people would not consider the improvement practically significant.

Type II error

Accepting the null hypothesis when it is false

Example

In a t-test for a sample mean µ, with null hypothesis "µ = 0" and alternate hypothesis "µ > 0", we may talk about the Type II error relative to the general alternate hypothesis "µ > 0", or may talk about the Type II error relative to the specific alternate hypothesis "µ > 1". Note that the specific alternate hypothesis is a special case of the general alternate hypothesis.



Chapter 10

Problem 1)

Solution

Using Excel Stat Analysis tool: Sample mean = 8.75 and s = 4.7337

Established mean for the publication of others that have taken this test of 6.

T-test score = = 3.1819

Mean of the sample was 8.75

Yes, the test is highly significant at 99%.

The null and alternate hypothesis are

H0: µ = 6

H1: µ >= 6

Reject the null hypothesis as critical value is larger than the tabulated value at 99% i.e. 3.1819 > 2.76

Problem 2)

Solution

Sample 1: m ...