Math 533 Aj Davis Part B
Problem N°1
1.Formulate the null and alternative hypotheses.
Null Hypothesis: The average (mean) annual income was greater than or equal to $50,000
H_0: μ≥50000
Alternate Hypothesis: The average (mean) annual income was less than $50,000.
H_a: μ 30 we will use the z-test.
As Ha:μ0.40 the, test is a right tailed z-test.
The critical value for significance level, α=0.05 for a right tailed z-test is given in the table as: 1.645.
Decision Rule: Reject H_0,if z>1.645
3. Calculate the test statistic.
In order to do the calculations by hand, we have p hat = (0.4*50)/50=0.4 and q=1-0.4=0.6 and n=50. P>0.4 mean that 21/50=0.42 then p > 0.42
Z- test statistic: z= (phat- P0 )/√((po*q)/n) = (0.4-0.42)/(/√((0.4*0.6)/50)) = -0.2887
4. Compare the test statistic to the rejection region and make a judgment about the null hypothesis.
Reject H_0,if z>1.645
-0.2887alpha(0.05) which mean that we fail to reject H0.
7. Based on the p-value, what decision would you make concerning the null hypothesis? Why?
Since the P-value (0.386) is greater than the significance level (0.05), we fail to reject the null hypothesis. The p-value implies the probability of rejecting a true null hypothesis.
At a significance level of 0.05, there is no sufficient evidence to support the claim that the true population proportion of customers who live in an urban area is greater than 40%.
Problem N°3: The average (mean) number of years lived in the current home is less than 13 years.
1.Formulate the null and alternative hypotheses.
Null Hypothesis: The average (mean) number of years lived in the current home is greater than or equal to 13 years
H_0: μ≥13
Alternate Hypothesis: The average (mean) number of years lived in the current home is less than 13 years.
H_a: μ 30 we will use the z-test.
As the Ha:μ alpha(0.05) which mean that we fail to reject H0.
7. Based on the p-value, what decision would you make concerning the null hypothesis? Why?
Since the P-value (0.152)
1.Formulate the null and alternative hypotheses.
Null Hypothesis: The average (mean) annual income was greater than or equal to $50,000
H_0: μ≥50000
Alternate Hypothesis: The average (mean) annual income was less than $50,000.
H_a: μ 30 we will use the z-test.
As Ha:μ0.40 the, test is a right tailed z-test.
The critical value for significance level, α=0.05 for a right tailed z-test is given in the table as: 1.645.
Decision Rule: Reject H_0,if z>1.645
3. Calculate the test statistic.
In order to do the calculations by hand, we have p hat = (0.4*50)/50=0.4 and q=1-0.4=0.6 and n=50. P>0.4 mean that 21/50=0.42 then p > 0.42
Z- test statistic: z= (phat- P0 )/√((po*q)/n) = (0.4-0.42)/(/√((0.4*0.6)/50)) = -0.2887
4. Compare the test statistic to the rejection region and make a judgment about the null hypothesis.
Reject H_0,if z>1.645
-0.2887alpha(0.05) which mean that we fail to reject H0.
7. Based on the p-value, what decision would you make concerning the null hypothesis? Why?
Since the P-value (0.386) is greater than the significance level (0.05), we fail to reject the null hypothesis. The p-value implies the probability of rejecting a true null hypothesis.
At a significance level of 0.05, there is no sufficient evidence to support the claim that the true population proportion of customers who live in an urban area is greater than 40%.
Problem N°3: The average (mean) number of years lived in the current home is less than 13 years.
1.Formulate the null and alternative hypotheses.
Null Hypothesis: The average (mean) number of years lived in the current home is greater than or equal to 13 years
H_0: μ≥13
Alternate Hypothesis: The average (mean) number of years lived in the current home is less than 13 years.
H_a: μ 30 we will use the z-test.
As the Ha:μ alpha(0.05) which mean that we fail to reject H0.
7. Based on the p-value, what decision would you make concerning the null hypothesis? Why?
Since the P-value (0.152)