Given the following hypotheses A random sample of five resul

Given the following hypotheses:

A random sample of five resulted in the following values: 18, 15, 12, 19, and 21. Assume a normal population. Using the .01 significance level, can we conclude the population mean is less than 20?

b.

Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Solution

Answer to the question)

Sample size n = 5

Sample mean x bar = (18+15+12+19+21)/5

x bar = 17

likewise , sample standard deviation s= 3.54

.

it is a left tailed test

we got M = 20

alpha = 0.01

.

the formula of test statistic is:

t = (x bar - M) / (s /srt(n))

.

On plugging the values we get

t = (17-20) / (3.54/sqrt(5))

t = -1.89

.

df = 5-1 = 4

.

The P value is : 0.0659 ..[can refer to t table to get the p value]

.

Inference: since the P value 0.0659 > alpha 0.01 , we fial to reject the null

Conclusion: Thus we conclude that the Mean is at least 20. It is not less than 20