Question

A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. 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, 67 seniors reported using drugs or alcohol within the past month, while 63 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 (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.)
  ---Select---tz =

• Part (f)

  What is the p-value? (Round your answer to four decimal places.)
  
  
  Explain what the p-value means for this problem.
• If H₀is 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 0.04 more than the proportion of students who use drugs and alcohol nationally.
• If H₀is true, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is 0.04 less than the proportion of students who use drugs and alcohol nationally.    
• If H₀is 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 0.04 more than the proportion of students who use drugs and alcohol nationally.
• If H₀is false, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is 0.04 less 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.)
  α = .05
  
  (ii) Decision:

  reject the null hypothesis

• do not reject the null hypothesis    

  
  (iii) Reason for decision:

  Since p-value > α, we do not reject the null hypothesis.

• Since p-value > α, we reject the null hypothesis.   

• Since p-value < α, we reject the null hypothesis.

• Since p-value < α, 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 standard normal distribution will be used because the samples involve the difference in proportions.

• 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.

Answer 1

We will conduct a Z test for two proportion

d) Distribution is normal

e-f)test statistic and p-value can be found if you follow the right steps to conduct this hypothesis below

option C is right

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 0.04 more than the proportion of students who use drugs and alcohol nationally.

g)

h)

ii)Do not reject the null hypothesis as P value > significance level

iii)

Since p-value > α, we do not reject the null hypothesis.

iv)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.    

v)The standard normal distribution will be used because the samples involve the difference in proportions.