Determine if the conditions required for the normal approximation to the binomial are met. If so, perform a full hypothesis test on the claim.

In a pre-health statistics course, approximately 25% of the students fail the test on hypothesis testing. A professor implements a new method for teaching the material and wishes to test whether this method significantly changes the number of students who fail the test. She uses the new method in all three of her classes, and gives the same test to all 100 students across her three sections of the course, of which 14 fail the test. Test the professor's claim at the 10% level of significance.

Standard Normal Distribution Table

a.Compute the value of the test statistic and its corresponding p-value. z=________(Round to 2 decimal places)

p=________(Round to 4 decimal places)

Enter 0 for both if cannot use normal approximation to binomial.

b.Conclude whether to reject the null hypothesis or not based on the p-value.

Reject

Fail to Reject

Cannot Use Normal Approximation to Binomial

Question 2

A professor believes that the majority of students at the college are in favour of having more private health-care options available, so long as the public health-care system doesn't decrease or diminish in any way. He takes a poll of 50 randomly-selected students at the college, asking the following question: Are you in favour of more private health-care options, if the current public health-care system is not decreased or diminished in any way? The results are recorded below:

N	Y	Y	Y	Y	Y	N	N	Y	Y
Y	N	N	N	Y	Y	N	Y	Y	Y
Y	N	N	N	Y	N	Y	N	Y	N
Y	Y	Y	Y	N	N	Y	Y	N	Y
Y	N	Y	Y	Y	N	N	N	Y	Y

Test the professor's claim that the majority of students are in favour of more private health-care options available at the 5% level of significance.

Standard Normal Distribution Table

a.Compute the value of the test statistic and its corresponding p-value. z=________(Round to 2 decimal places)

p=_________(Round to 4 decimal places)

Enter 0 for both if cannot use normal approximation to binomial.

b.Conclude whether to reject the null hypothesis or not based on the p-value.

Reject

Fail to Reject

Cannot Use Normal Approximation to Binomial

Question 3

A female patient with anemia (iron deficiency) has her hemoglobin levels measured once a month for 4 years, as her physician wants to monitor her condition. The patient's mean hemoglobin concentration over the 4 years is 7.85 g per dL of blood. The physician informs the patient that her condition has progressed to severe anemia, which is characterized by hemoglobin levels of less than 8 g/dL. If the standard deviation for hemoglobin levels for women is 0.75 g/dL, test the physician's claim that the patient's condition has progressed to severe anemia at the 10% level of significance.

Standard Normal Distribution Table

a.Compute the value of the test statistic and its corresponding p-value. z=________(Round to 2 decimal places)

p=________(Round to 4 decimal places)

b.Conclude whether to reject the null hypothesis or not based on the p-value.

Reject

Fail to Reject

Question 4

H0:=12.5

H1:12.5

xsn=14.45=3.12=18=0.01

Standard Normal Distribution Table

T-Distribution Table

a.Compute the value of the test statistic and determine the corresponding p-value bounds using the t-distribution table. t=______(Round to 3 decimal places)

________< p <_______

b.Conclude whether to reject the null hypothesis or not based on the p-value.

Reject

Fail to Reject

Question 5

The average nurse spends 1.3 hours on paperwork during every 8-hour shift. A new procedure is implemented with the hopes of reducing this time. However, given the high cost of changing procedures, the administration wants to be as certain as possible that the new system will actually reduce the time spent on paperwork before making the change.

a.Determine what population parameter is being tested:

p

(rho)

b.Determine if the alternative hypothesis is a left-tailed, right-tailed, or two-tailed test:

< : left-tailed

> : right-tailed

: two-tailed

c.Determine the most appropriate level of significance to use: 1%, 5%, or 10%

1%

5%

10%

Question 6

Determine if the conditions required for the normal approximation to the binomial are met. If so, calculate the test statistic, determine the p-value of the test statistic for the hypothesis test, and use that to decide whether there is sufficient evidence to reject the null hypothesis or not at the given level of significance.

H0:p=0.333

H1:p>0.333

xn=60=150=0.05

Standard Normal Distribution Table

a.Compute the value of the test statistic and its corresponding p-value. z=________(Round to 2 decimal places)

p=________(Round to 4 decimal places)

Enter 0 for both if cannot use normal approximation to binomial.

b.Conclude whether to reject the null hypothesis or not based on the p-value.

Reject

Fail to Reject

Cannot Use Normal Approximation to Binomial

Question 7

A nurse is monitoring the bilirubin levels in an elderly patient who appears to be jaundiced (in mg/dL):

3.1	3.5	2.8	3.3	2.6	3.4
2.7	2.4	2.9	3.2	3.3	3

Note: The data appears to be approximately normally distributed.

Patients with bilirubin levels above 3 mg/dL are considered to be jaundiced, which can be pose a serious health problem. Test the claim that this patient is jaundiced at the 5% level of significance.

Standard Normal Distribution Table

T-Distribution Table

a.Calculate the sample mean and standard deviation. x=________(Round to 3 decimal places)

s=__________(Round to 3 decimal places)

b.Compute the value of the test statistic and and determine the corresponding p-value bounds using the t-distribution table and your answers from part (a). t=_______(Round to 3 decimal places)

p >________

c.Conclude whether to reject the null hypothesis or not based on the p-value.

Reject

Fail to Reject

Question 8

Test the claim that the average recovery time for a certain operation is 4 weeks (measured by when the patient can fully return to normal daily activities), if a sample of 69 patient recovery times are collected, with a sample mean of 4.45 weeks and a sample standard deviation of 1.32 weeks. Use a 1% level of significance.

Standard Normal Distribution Table

T-Distribution Table

a.Compute the value of the test statistic and its corresponding p-value. t=_______(Round to 3 decimal places)

p <________

b.Conclude whether to reject the null hypothesis or not based on the p-value.

Reject

Fail to Reject

Question 9

H0:=211.4F H1:211.4F Level of significance:=0.01 Sample size:n=122 Sample mean:x=210.1F Known population standard deviation:=4.75F Unknown distribution of population data

Standard Normal Distribution Table

a.Compute the value of the test statistic and its corresponding p-value. z=________(Round to 2 decimal places)

p=_______(Round to 4 decimal places)

b.Conclude whether to reject the null hypothesis or not based on the p-value.

Reject

Fail to Reject

c.State the decision error type that is possible.

Type I Error

Type II Error