Question

When 3015 adults were surveyed in a​ poll, 73​% said that they use the internet. is it okay for a newspaper reporter to write that ​"3 divided by 4 of all adults use the​ internet"? why or why​ not? identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim?

Answer 1

Answer:

Claim is rejected

Step-by-step explanation:

Solution:-

- The claim was made by the newspaper reporter " 3 divided by 4 of all adults use the​ internet "  the proportion of people who are claimed to use internet are p = 0.75.

- A random sample was taken of N = 305 individuals were surveyed in a poll.

- We are to test the claim made by the reporter for the sample N.

- State the hypothesis for the effectiveness of medication:

         Null Hypothesis: p = 0.75  

         Alternate hypothesis: p ≠ 0.75  

- The conditions of standard normality:

         n*p > 5 , 3015*0.75 = 2261.25 > 5   .. ( Ok )

         n*(1-p) > 5 , 3015*0.25 = 753.75 > 5 .. ( Ok )

The standard normal test is applicable since normal approximation to binomial distribution for a fairly large sample size N = 3015 adults.

Assuming the population proportion to be normally distributed.

- We will estimate the population proportion with the sample proportion obtained from a poll survey p* = 0.73

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

                        $Z-test = \frac{p* - p}{\sqrt{p*( 1 -p) / N} } \\\\Z-test = \frac{0.73 - 0.75}{\sqrt{0.75*0.25 / 3015} } \\\\Z-test = -\frac{0.02}{0.00788 } \\\\Z-test = -2.53807$

- 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 not equal to the reporter's claimed value. So, the rejection region defined by the lower and upper tail of the standard normal.

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

                      P ( Z < ±Z-critical ) = α / 2 = 0.025

                      Z-critical = ± 1.96

- The rejected values all lie to the left or right of the Z-critical value ±1.96          

- The claim test value is compared the rejection region:

                     -2.53807 < -1.96

                      Z-test < Z-critical

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

Conclusion:

The Null hypothesis or claim made by the reporter that 3 out of 4 adults use internet i.e 75% use internet is without sufficient evidence. Hence, the claim made is false or has no statistical evidence.