Question

Assignment #6 Due Sunday by 11:55pm 1. The following 10 numbers were drawn from a population. Is it likely that these numbers came from a population with a mean of 13? Evaluate with a two-tailed test at p < .05. 5, 7, 7, 10, 10, 10, 11, 12, 12, 13

a. State both in words, and then symbolically what your H1 and H0 would be.

b. What is your df? What is your critical t?

c. Calculate t

d. Based on the above information, would you reject H0, or fail to reject it? Why? How would you state your conclusion in words?

e. Bonus Credit: Calculate the 95% confidence interval for the alternative hypothesis distribution.

Answer 1

a) Let denotes the population mean.

To test against against

Here

sample mean

sample standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 5% level of significance if

Now,

The value of the test statistic

degrees of freedom (df) = 10 - 1 = 9

and critical value

d) Since , so we reject H₀ at 5% level of significance and we can conclude that population mean is significantly from 13.

e) a 95% confidence interval for population mean