Question

A manufacturer of a new medication on the market for Parkinson's disease makes a claim that the medication is effective in 75% of people who have the disease. One hundred fifty individuals with Parkinson's disease are given the medication, and 100 of them note the medication was effective. Does this finding provide statistical evidence at the 0.05 level that the effectiveness is less than the 75% claim the company made? Make sure to include parameter, conditions, calculations, and a conclusion in your answer.

Answer 1

Answer:

Claim is rejected

Step-by-step explanation:

Solution:-

- The claim was made on the effectiveness of medication on the market of Parkinson's disease to be p = 75%.

- A random sample was taken of N = 150 individuals and n = 100 number of people reported that it was effectively.

- We are to test the claim made by the manufacturer of the medication based on the statistics available for the sample N.

- State the hypothesis for the effectiveness of medication:

          Null Hypothesis: p = 0.75   ... Claim

          Alternate hypothesis: p < 0.75   .... Test

- The conditions of standard normality:

• n*p > 5 , 150*0.75 = 112.5   .. ( Check )

• n*(1-p) > 5 , 150*0.25 = 37.5  .. ( Check )

Hence, the standard normal test is applicable. Assuming the population proportion to be normally distributed.

- We will estimate the population proportion with the sample proportion ( p* ):

                          p* = n / N

                          p* = 100 / 150

                          p* = 2/3 = 0.667

- Testing against the claimed population proportion ( p ) = 0.75. The standard normal statistic value is given by:

                         $Z-test= \frac{(p^* - p)}{\sqrt{p(1-p) / N} } \\\\Z-test= \frac{(0.6667 - 0.75)}{\sqrt{0.75(0.25) / 150} } \\\\Z-test= \frac{-0.0833}{\sqrt{0.00125} } \\\\Z-test= -2.35607$

- We will see whether the Z-test statistic falls in the rejection region defined by the critical value of Z at significance level ( α ) of 0.05.

- The rejection region is defined by the Alternate hypothesis which is less than the claimed value. So, the rejection region defined by the lower tail of the standard normal.

- So for lower tailed test the critical value of statistics is:

                       P ( Z < Z-critical ) = α = 0.05

                       Z-critical = - 1.645

- The rejected values all lie to the left of the Z-critical value -1.645          

- The claim test value is compared the rejection region:

                      -2.35607 < -1.645

                       Z-test < Z-critical

Hence, Null hypothesis rejected because test lies in the rejection region.

Conclusion:

The Null hypothesis or claim made by the manufacturer of Parkinson's disease medication of 75% effectiveness is without sufficient evidence. Hence, the claim made is false or has no statistical evidence.