Question

ion 1, fi 3. Draw a sample of X from question 2 and below is the data set: 1 1.5 2.1 2.6 1.9 a. Find the mean and standard deviation of the sample. b. Calculate the confidence interval of the mean. c. Perform a t test to test if the mean equals 2 or not.

Answer 1

a) Here

sample mean

sample standard deviation

and sample size

5

b) a 95% confidence interval for true mean

(7 *to.025,n-1 Vn *to.o25,n-1,T+ V n +m

0,00to.os.4 vS 0.025,4 0.025.4, 1.8240506 = ( 1.82--* t0.025.4, 0.025,4 1.O4

c) To test against

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

obs| ノ 10.025, n-1

Now,

The value of the test statistic

and critical value

Since , so we fail to reject H₀ at 5% level of significance and we can conclude that the true mean is not significantly different from 2.