Using the. 05 significance level

1. 
   A sample of 36 observations is selected from a normal population. The sample mean is
   

49, and the population standard deviation is 5. Conduct the following test of hypothesis
using the .05 significance level.

1. 
   Is this a one- or two-tailed test? Two-tailed.
   
2. 
   What is the decision rule? 0.05/2=0.025=p; => 0.5-0.025=0.475; => z₀=1.96 (-1.96)
   
3. 
   What is the value of the test statistic?
   
4. 
   What is your decision regarding H0? fail to reject
   
5. 
   What is the p-value? Interpret it. p(1.2)=0.3849; 0.5-0.3849=0.1151; for two-tailed: 0.1151*2=0.2302
   

2. 
   A sample of 36 observations is selected from a normal population. The sample mean is
   

12, and the population standard deviation is 3. Conduct the following test of hypothesis
using the .02 significance level.

1. 
   Is this a one- or two-tailed test? One-tailed test.
   
2. 
   What is the decision rule? 0.5-0.02=0.048; => z₀=2.05
   
3. 
   What is the value of the test statistic?
   
4. 
   What is your decision regarding H0? rejected
   
5. 
   What is the p-value? Interpret it. p(4)=1-0.5-0.5=0
   

3. 
   Given the following hypothesis:
   

A random sample of 12 observations is selected from a normal population. The sample
mean was 407 and the sample standard deviation 6. Using the .01 significance level:
a. State the decision rule.
b. Compute the value of the test statistic.
c. What is your decision regarding the null hypothesis?

4. The mean income per person in the United States is $40,000, and the distribution of incomes follows a normal distribution. A random sample of 10 residents of Wilmington, Delaware, had a mean of $50,000 with a standard deviation of $10,000. At the .05 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average?