Question

*****Please answer all questions*****

Question 1 (1 point)

Consumers Energy states that the average electric bill across the state is $39.09. You want to test the claim that the average bill amount is actually different from $39.09. What are the appropriate hypotheses for this test?

Question 1 options:

	1) HO: μ ≥ 39.09 HA: μ < 39.09
	2) HO: μ ≠ 39.09 HA: μ = 39.09
	3) HO: μ ≤ 39.09 HA: μ > 39.09
	4) HO: μ > 39.09 HA: μ ≤ 39.09
	5) HO: μ = 39.09 HA: μ ≠ 39.09

Question 2 (1 point)

A medical researcher wants to determine if the average hospital stay after a certain procedure is greater than 12.41 days. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≤ 12.41, Alternative Hypothesis: μ > 12.41. If the researcher randomly samples 22 patients that underwent the procedure and determines their average hospital stay was 14.93 days with a standard deviation of 6.108 days, what is the test statistic and p-value of this test?

Question 2 options:

	1) Test Statistic: 1.935, P-Value: 0.9667
	2) Test Statistic: 1.935, P-Value: 0.0666
	3) Test Statistic: -1.935, P-Value: 0.9667
	4) Test Statistic: -1.935, P-Value: 0.0333
	5) Test Statistic: 1.935, P-Value: 0.0333

Question 3 (1 point)

Suppose the national average dollar amount for an automobile insurance claim is $566.2. You work for an agency in Michigan and you are interested in whether or not the state average is different from the national average. The hypotheses for this scenario are as follows: Null Hypothesis: μ = 566.2, Alternative Hypothesis: μ ≠ 566.2. A random sample of 89 claims shows an average amount of $574.113 with a standard deviation of $83.7792. What is the test statistic and p-value for this test?

Question 3 options:

	1) Test Statistic: 0.891, P-Value: 1.8123
	2) Test Statistic: 0.891, P-Value: 0.8124
	3) Test Statistic: 0.891, P-Value: 0.3753
	4) Test Statistic: -0.891, P-Value: 0.3753
	5) Test Statistic: 0.891, P-Value: 0.18765

Question 4 (1 point)

It is reported in USA Today that the average flight cost nationwide is $414.79. You have never paid close to that amount and you want to perform a hypothesis test that the true average is actually less than $414.79. The hypotheses for this situation are as follows: Null Hypothesis: μ ≥ 414.79, Alternative Hypothesis: μ < 414.79. You take a random sample of national flight cost information and perform a one sample mean hypothesis test. You observe a p-value of 0.342. What is the appropriate conclusion? Conclude at the 5% level of significance.

Question 4 options:

	1) We did not find enough evidence to say a significant difference exists between the true average flight cost and $414.79.
	2) The true average flight cost is greater than or equal to $414.79.
	3) We did not find enough evidence to say the true average flight cost is greater than $414.79.
	4) The true average flight cost is significantly less than $414.79.
	5) We did not find enough evidence to say the true average flight cost is less than $414.79.

Question 5 (1 point)

Consumers Energy states that the average electric bill across the state is $124.59. You want to test the claim that the average bill amount is actually greater than $124.59. The hypotheses for this situation are as follows: Null Hypothesis: μ ≤ 124.59, Alternative Hypothesis: μ > 124.59. You complete a randomized survey throughout the state and perform a one-sample hypothesis test for the mean, which results in a p-value of 0.0187. What is the appropriate conclusion? Conclude at the 5% level of significance.

Question 5 options:

	1) The true average electric bill is less than or equal to $124.59.
	2) The true average electric bill is significantly greater than $124.59.
	3) The true average electric bill is significantly different from $124.59.
	4) We did not find enough evidence to say the true average electric bill is greater than $124.59.
	5) The true average electric bill is significantly less than $124.59.

Answer 1

Question 1

Question 2

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 14.93 - 12.41 ) / ( 6.108 / √(22) )
t = 1.9351

P - value = P ( t > 1.9351 ) = 0.0333

Question 3

Test Statistic :-
t = ( X̅ - µ ) / ( S / √(n))
t = ( 574.113 - 566.2 ) / ( 83.7792 / √(89) )
t = 0.891

P - value = P ( t > 0.891 ) = 0.3753

Question 4

Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.342 > 0.05 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

Question 5

Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.0187 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis