Consider the following hypothesis test: H0: µ = 20
Ha: µ < 20
A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.
a. Compute the value of the test statistic (to 2 decimals).
b. What is the p-value (to 3 decimals)?
c. Using a = .05, can it be concluded that the population mean is less than 20?
d. Using a = .05, what is the critical value for the test statistic?
e. State the rejection rule: Reject H0 if z is the critical value.
f. Using a = .05, can it be concluded that the population mean is less than 20?

a

b

c

There is sufficient evidence to show that the population mean is less than 20

d

e

   The decision rule is  

Reject the null hypothesis

f

The conclusion is  

  There is sufficient evidence to show that the population mean is less than 20.

Step-by-step explanation:

From the question we are told that

   The null hypothesis  is  

    The alternative hypothesis is  Ha: µ < 20

    The sample size is  n  =  50  

    The sample mean is  

    The level of significance is  

      The population standard deviation is  

Generally the test statistics is mathematically represented as

=>    

=>    

From the z table  the area under the normal curve to the left corresponding to  -2.12  is  

Generally the p-value is  

From values obtained we see that hence  

   The decision rule is  

Reject the null hypothesis

   The conclusion is  

  There is sufficient evidence to show that the population mean is less than 20.

Generally form the normal distribution table the critical value at a level of significance of   is

Generally given that  

   The decision rule is  

Reject the null hypothesis

   The conclusion is  

  There is sufficient evidence to show that the population mean is less than 20.

50=33x+22

step-by-step explanation: