Question

Consider the following hypothesis test: H 0: 20 H a: < 20 A sample of 55 provided a sample mean of 19.6. The population standard deviation is 1.6.

a. Compute the value of the test statistic (to 2 decimals). If your answer is negative, use minus "-" sign.

b. What is the p-value (to 3 decimals)? c. Using = .05, can it be concluded that the population mean is less than 20?

d. Using = .05, what is the critical value for the test statistic (to 3 decimals)? If your answer is negative, use minus "-" sign.What is the rejection rule using the critical value? Reject H 0 if z

e. What is your conclusion? Reject H 0 if z is the critical value.

Answer 1

a)
Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (19.6 - 20)/(1.6/sqrt(55))
z = -1.85

b)
P-value Approach
P-value = 0.032

c)
As P-value < 0.05, reject the null hypothesis.
yes it can be concluded

d)
This is left tailed test, for α = 0.05
Critical value of z is -1.645.

e)
Reject the null hypothesis
Hence reject H0 if z < -1.645