A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percentage. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally, 65 seniors reported using drugs or alcohol within the past month, while 60 national seniors reported using them. Conduct a hypothesis test at the 5% level. NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) State the null hypothesis. H0: plocal ≠ pnational H0: plocal > pnational H0: plocal = pnational H0: plocal < pnational Part (b) State the alternative hypothesis. Ha: plocal < pnational Ha: plocal = pnational Ha: plocal ≠ pnational Ha: plocal > pnational Part (c) In words, state what your random variable P'local − P'national represents. a.P'local − P'national represents the average difference of drug and alcohol abuse of local seniors and national seniors. b. P'local − P'national represents the difference in proportions of seniors who use drugs and seniors who use alcohol. c.P'local − P'national represents the difference in proportions of drug and alcohol abuse of local seniors and national seniors. d.P'local − P'national represents the difference in the average amount of drug and alcohol abuse of local seniors and national seniors. Part (d) State the distribution to use for the test. (Round your answers to four decimal places.) P'local − P'national ~ =, =,= Part (e) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.) = Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. If H0 is false, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is 0.05 less than the proportion of students who use drugs and alcohol nationally.If H0 is true, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is 0.05 less than the proportion of students who use drugs and alcohol nationally. If H0 is false, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is at least 0.05 more than the proportion of students who use drugs and alcohol nationally.If H0 is true, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is at least 0.05 more than the proportion of students who use drugs and alcohol nationally. Part (g) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) ? = (ii) Decision: reject the null hypothesis do not reject the null hypothesis (iii) Reason for decision: Since p-value > ?, we do not reject the null hypothesis. Since p-value > ?, we reject the null hypothesis. Since p-value < ?, we reject the null hypothesis.Since p-value < ?, we do not reject the null hypothesis. (iv) Conclusion: There is sufficient evidence to show that the proportion of local seniors using drugs and alcohol locally is higher than the proportion of seniors using drugs and alcohol nationally. There is not sufficient evidence to show that the proportion of local seniors using drugs and alcohol locally is higher than the proportion of seniors using drugs and alcohol nationally. Part (i) Explain how you determined which distribution to use. The t-distribution will be used because the samples are independent and the population standard deviation is not known. The t-distribution will be used because the samples are dependent. The standard normal distribution will be used because the samples are independent and the population standard deviation is known. The standard normal distribution will be used because the samples involve differences in proportions.

A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percentage. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally, 65 seniors reported using drugs or alcohol within the past month, while 60 national seniors reported using them. Conduct a hypothesis test at the 5% level. NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) State the null hypothesis. H0: plocal ≠ pnational H0: plocal > pnational H0: plocal = pnational H0: plocal < pnational Part (b) State the alternative hypothesis. Ha: plocal < pnational Ha: plocal = pnational Ha: plocal ≠ pnational Ha: plocal > pnational Part (c) In words, state what your random variable P'local − P'national represents. a.P'local − P'national represents the average difference of drug and alcohol abuse of local seniors and national seniors. b. P'local − P'national represents the difference in proportions of seniors who use drugs and seniors who use alcohol. c.P'local − P'national represents the difference in proportions of drug and alcohol abuse of local seniors and national seniors. d.P'local − P'national represents the difference in the average amount of drug and alcohol abuse of local seniors and national seniors. Part (d) State the distribution to use for the test. (Round your answers to four decimal places.) P'local − P'national ~ =, =,= Part (e) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.) = Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. If H0 is false, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is 0.05 less than the proportion of students who use drugs and alcohol nationally.If H0 is true, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is 0.05 less than the proportion of students who use drugs and alcohol nationally. If H0 is false, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is at least 0.05 more than the proportion of students who use drugs and alcohol nationally.If H0 is true, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is at least 0.05 more than the proportion of students who use drugs and alcohol nationally. Part (g) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) ? = (ii) Decision: reject the null hypothesis do not reject the null hypothesis (iii) Reason for decision: Since p-value > ?, we do not reject the null hypothesis. Since p-value > ?, we reject the null hypothesis. Since p-value < ?, we reject the null hypothesis.Since p-value < ?, we do not reject the null hypothesis. (iv) Conclusion: There is sufficient evidence to show that the proportion of local seniors using drugs and alcohol locally is higher than the proportion of seniors using drugs and alcohol nationally. There is not sufficient evidence to show that the proportion of local seniors using drugs and alcohol locally is higher than the proportion of seniors using drugs and alcohol nationally. Part (i) Explain how you determined which distribution to use. The t-distribution will be used because the samples are independent and the population standard deviation is not known. The t-distribution will be used because the samples are dependent. The standard normal distribution will be used because the samples are independent and the population standard deviation is known. The standard normal distribution will be used because the samples involve differences in proportions.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

Part (a)

State the null hypothesis.

H₀: p_local ≠ p_national

H₀: p_local > p_national

H₀: p_local = p_national

H₀: p_local < p_national
Part (b)

State the alternative hypothesis.

H_a: p_local < p_national

H_a: p_local = p_national

H_a: p_local ≠ p_national

H_a: p_local > p_national
Part (c)

In words, state what your random variable
P'_local − P'_national
represents.

a.P'_local − P'_nationalrepresents the average difference of drug and alcohol abuse of local seniors and national seniors.

b. P'_local − P'_nationalrepresents the difference in proportions of seniors who use drugs and seniors who use alcohol.

c.P'_local − P'_nationalrepresents the difference in proportions of drug and alcohol abuse of local seniors and national seniors.

d.P'_local − P'_nationalrepresents the difference in the average amount of drug and alcohol abuse of local seniors and national seniors.
Part (d)

State the distribution to use for the test. (Round your answers to four decimal places.)

P'_local − P'_national
~ =, =,=
Part (e)

What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)
=
Part (f)

What is the p-value? (Round your answer to four decimal places.)

Explain what the p-value means for this problem.
If
H₀ is false, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is 0.05 less than the proportion of students who use drugs and alcohol nationally.If

H₀ is true, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is 0.05 less than the proportion of students who use drugs and alcohol nationally. If

H₀ is false, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is at least 0.05 more than the proportion of students who use drugs and alcohol nationally.If

H₀ is true, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is at least 0.05 more than the proportion of students who use drugs and alcohol nationally.
Part (g)

Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value.
Part (h)

Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
? =

(ii) Decision:
reject the null hypothesis do not reject the null hypothesis

(iii) Reason for decision:
Since p-value > ?, we do not reject the null hypothesis. Since p-value > ?, we reject the null hypothesis.    Since p-value < ?, we reject the null hypothesis.Since p-value < ?, we do not reject the null hypothesis.

(iv) Conclusion:
There is sufficient evidence to show that the proportion of local seniors using drugs and alcohol locally is higher than the proportion of seniors using drugs and alcohol nationally. There is not sufficient evidence to show that the proportion of local seniors using drugs and alcohol locally is higher than the proportion of seniors using drugs and alcohol nationally.
Part (i)

Explain how you determined which distribution to use.
The t-distribution will be used because the samples are independent and the population standard deviation is not known. The t-distribution will be used because the samples are dependent. The standard normal distribution will be used because the samples are independent and the population standard deviation is known. The standard normal distribution will be used because the samples involve differences in proportions.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here