math-225n-FINAL EXAM, Exams of Nursing

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1/1 POINTS

A fitness center claims that the mean amount of time that a person spends at the gym

per visit is 33 minutes. Identify the null hypothesis, H 0 , and the alternative

hypothesis, Ha, in terms of the parameter μ.

That is correct! H 0 : μ≠33; Ha: μ= H 0 : μ=33; Ha: μ≠ H 0 : μ≥33; Ha: μ< H 0 : μ≤33; Ha: μ>

Answer Explanation

Correct answer:

Let the parameter μ be used to represent the mean. The null hypothesis is always

stated with some form of equality: equal (=), greater than or equal to (≥), or less than or equal to (≤). Therefore, in this case, the null hypothesis H 0 is μ=33. The alternative hypothesis is contradictory to the null hypothesis, so Ha is μ≠33.

QUESTION 21/1 POINTS

The answer choices below represent different hypothesis tests. Which of the choices are right-tailed tests? Select all correct answers. That is correct!   

H 0 :X≥17.1, Ha:X<17.

H 0 : μ=33; Ha: μ≠

     

H 0 :X=14.4, Ha:X≠14.

H 0 :X≤3.8, Ha:X>3. H 0 :X≤7.4, Ha:X>7. H 0 :X=3.3, Ha:X≠3.

   Answer Explanation Correct answer: Remember the forms of the hypothesis tests.

 Right-tailed: H 0 :X≤X 0 , Ha:X>X 0.

 Left-tailed: H 0 :X≥X 0 , Ha:X<X 0.  Two-tailed: H 0 :X=X 0 , Ha:X≠X 0. H 0 :X≤3.8, Ha:X>3. H 0 :X≤7.4, Ha:X>7.

 

0/1 POINTS

Find the Type II error given that the null hypothesis, H 0 , is: a building inspector claims

that no more than 15% of structures in the county were built without permits.

That's not right. The building inspector thinks that no more than 15% of the structures in the county were built without permits when, in fact, no more than 15% of the structures really were built without permits. The building inspector thinks that more than 15% of the structures in the county were built without permits when, in fact, more than 15% of the structures really were built without permits. The building inspector thinks that more than 15% of the structures in the county were built without permits when, in fact, at most 15% of the structures were built without permits. The building inspector thinks that no more than 15% of the structures in the county were built without permits when, in fact, more than 15% of the structures were built without permits.

Answer Explanation

Correct answer: A Type II error is the decision not to reject the null hypothesis when, in fact, it is false. In this case, the Type II error is when the building inspector thinks that no more

than 15% of the structures were built without permits when, in fact, more than 15% of

the structures were built without permits. Your answer:

The building inspector thinks that more than 15% of the structures in the county were

built without permits when, in fact, at most 15% of the structures were built without

permits.

The building inspector thinks that no more than 15% of the structures in the county

were built without permits when, in fact, more than 15% of the structures were built

without permits.

Content attribution- Opens a dialog

1/1 POINTS

What is the p-value of a right-tailed one-mean hypothesis test, with a test statistic

of z 0 =1.74? (Do not round your answer; compute your answer using a value from the table

below.)

z1.51.61.71.81.90.000.9330.9450.9550.9640.9710.010.9340.9460.9560.

9650.9720.020.9360.9470.9570.9660.9730.030.9370.9480.9580.9660. 730.040.9380.9490.9590.9670.9740.050.9390.9510.9600.9680.9740. 0.9410.9520.9610.9690.9750.070.9420.9530.9620.9690.9760.080.9430. 9540.9620.9700.9760.090.9440.9540.9630.9710.

That is correct! $$0.

Answer Explanation

Correct answers:  $0.041$0.

The p-value is the probability of an observed value of z=1.74 or greater if the null

hypothesis is true, because this hypothesis test is right-tailed. This probability is equal to

the area under the Standard Normal curve to the right of z=1.74.

A standard normal curve with two points labeled on the horizontal axis. The mean is labeled at 0.00 and an observed value of 1.74 is labeled. The area under the curve and to the right of the observed value is shaded.

In making the decision to reject or not reject H 0 , if α>p-value, reject H 0 because the

results of the sample data are significant. There is sufficient evidence to conclude

that H 0 is an incorrect belief and that the alternative hypothesis, Ha, may be correct.

If α≤p-value, do not reject H 0. The results of the sample data are not significant, so there is not sufficient evidence to conclude that the alternative hypothesis, Ha, may be correct. In this case, α=0. 04 is less than or equal to p=0.0401, so the decision is to

not reject the null hypothesis.

QUESTION 71/1 POINTS

A recent study suggested that 81% of senior citizens take at least one prescription

medication. Amelia is a nurse at a large hospital who would like to know whether the percentage is the same for senior citizen patients who go to her hospital. She randomly

selects 59 senior citizens patients who were treated at the hospital and finds that 49 of

them take at least one prescription medication. What are the null and alternative hypotheses for this hypothesis test? That is correct! {H 0 :p=0.81Ha:p>0. {H 0 :p≠0.81Ha:p=0. {H 0 :p=0.81Ha:p<0. {H 0 :p=0.81Ha:p≠0.

Answer Explanation

Correct answer:

{H 0 :p=0.81Ha:p≠0.

First verify whether all of the conditions have been met. Let p be the population

proportion for the senior citizen patients treated at Amelia's hospital who take at least one prescription medication.

1. Since there are two independent outcomes for each trial, the proportion follows a

binomial model.

2. The question states that the sample was collected randomly.

3. The expected number of successes, np=47.79, and the expected number of

failures, nq=n(1−p)=11.21, are both greater than or equal to 5.

Since Amelia is testing whether the proportion is the same, the null hypothesis is

that p is equal to 0.81 and the alternative hypothesis is that p is not equal to 0.81. The

null and alternative hypotheses are shown below.

{H 0 :p=0.81Ha:p≠0.

QUESTION 81/1 POINTS

A researcher claims that the proportion of cars with manual transmission is less

than 10%. To test this claim, a survey checked 1000 randomly selected cars. Of

those cars, 95 had a manual transmission.

The following is the setup for the hypothesis test:

{H 0 :p=0.10Ha:p<0.

Find the test statistic for this hypothesis test for a proportion. Round your answer

to 2 decimal places.

That is correct! $$Test_Statistic=−0. Answer Explanation Correct answers:  $\text{Test_Statistic}=-0.53$Test_Statistic=−0.

z=p^−p0p 0 ⋅(1−p 0 )n−−−−−−√

z=0.095−0.100.10⋅(1−0.10)1000−−−−−−−−√ z≈−0.

QUESTION 91/1 POINTS

A medical researcher claims that the proportion of people taking a certain medication that develop serious side effects is 12%. To test this claim, a random sample of 900 people taking the medication is taken and it is determined that 93 people have experienced serious side effects.. The following is the setup for this hypothesis test: H 0: p = 0.

Ha : p ≠ 0.

Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places. The following table can be utilized which provides areas under the Standard Normal Curve: z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.

• 1.8 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.030 0.
• 1.7 0.045 0.044 0.043 0.042 0.041 0.040 0.039 0.038 0.038 0.
• 1.6 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.
• 1.5 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.
• 1.4 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.

That is correct!

From a lookup table of the area under the Standard Normal curve, the corresponding area is then 2(0.062) = 0.124.

QUESTION 101/1 POINTS

An economist claims that the proportion of people who plan to purchase a fully electric

vehicle as their next car is greater than 65%.

To test this claim, a random sample of 750 people are asked if they plan to purchase a fully electric vehicle as their next car Of these 750 people, 513 indicate that they do

plan to purchase an electric vehicle. The following is the setup for this hypothesis test:

H 0 :p=0.

Ha:p>0. In this example, the p-value was determined to be 0.026.

Come to a conclusion and interpret the results for this hypothesis test for a proportion

(use a significance level of 5%.)

That is correct! The decision is to reject the Null Hypothesis. The conclusion is that there is enough evidence to support the claim. The decision is to fail to reject the Null Hypothesis. The conclusion is that there is not enough evidence to support the claim. Answer Explanation Correct answer: The decision is to reject the Null Hypothesis. The conclusion is that there is enough evidence to support the claim.

Since the p-value is greater than the level of significance, the conclusion is to reject thenull hypothesis.

QUESTION 11

1/1 POINTS

Becky's statistics teacher was teaching the class how to perform the z-test for a

proportion. Becky was bored because she had already mastered the test, so she decided to see if the coin she had in her pocket would come up heads or tails in a truly

random fashion when flipped. She discretely flipped the coin 30 times and got

heads 18 times. Becky conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of heads is different from 50%.

Which answer choice shows the correct null and alternative hypotheses for this test? That is correct! H 0 :p=0.6; Ha:p>0.6, which is a right-tailed test. H 0 :p=0.5; Ha:p<0.5, which is a left-tailed test. H 0 :p=0.6; Ha:p≠0.6, which is a two-tailed test. H 0 :p=0.5; Ha:p≠0.5, which is a two-tailed test.

Answer Explanation

Correct answer:

H 0 :p=0.5; Ha:p≠0.5, which is a two-tailed test.

The null hypothesis should be true proportion: H 0 :p=0.5. Becky wants to know if the true proportion of heads is different from 0.5. This means that we just want to test if the proportion is not 0.5. So, the alternative hypothesis is Ha:p≠0.5, which is a two-

tailed test.