Question

We want to test H0 : µ ≥ 200 versus Ha : µ < 200 . We know that n = 324, x = 199.700 and, σ = 6. We want to test H0 at the .05 level of significance. For this problem, round your answers to 3 digits after the decimal point.

1. What is the value of the test statistic?

2. What is the critical value for this test?

3. Using the critical value, do we reject or not reject H0?

4. What is the p-value for this test?

5. Using the p-value, do we reject or not reject H0?

Answer 1

Solution :

Given that,

This is a left (One) tailed test,

1)

The test statistics,

Z =( - )/ (/n)

= ( 199.400 - 200 ) / ( 6 / 324 )

= -0.900

2)

Critical value of  the significance level is α = 0.05, and the critical value for a left-tailed test is

= -1.645

3)

Since it is observed that z = -0.900 = -1.645 , it is then concluded that do not reject the null hypothesis.

4)

P- Value = P(Z < z )

= P(Z < -0.900)

= 0.1841

5)

The p-value is p = 0.1841, and since p =0.1841 0.05 , it is concluded that do not reject the null hypothesis.