Question

3. From SIRI to self-driving cars, artificial intelligence (Al) is progressing rapidly and changing our daily lifc in many ways. Ouc of the carly beucits of AT may be the climiuatiou of repctitive workplace tasks. Assume that 1,000 people were randomly selected in the United States and 510 of them support that AI will diminish the need for repcating tasks. Ts there evidence, at the .05 level of significance, that more than half of people in the U.S. support the idea that AI will diminish the need for repeating tasks? (a) Check the assumptions. (b) Write the null and alternative hypothesis. (c) Calculate the test statistic. (d) Find the p-value. (e) Make a decision and write a thorough interpretation. (f) Using the confidence interval approach to calculate a 95% two-sided confidence interval for p. Is the results of confidence interval consistent to the testing conclusion?

Answer 1

a. Here it is given that out of 1000 people, 510 of them support that AI will diminsh the need for repeating tasks.

So

As we see that n is sufficient large and also that np>10 also n(1-p)>10, we conclude that distribution is approximately normal.

b. Here claim is that more than half of the people in the US support the idea that AI will diminsh the need for repeating tasks. And as null hypothesis always have equality sign hypothesis here is

$H_0:p=0.5$ vs $H_1:p>0.5$

c. Here we have seen that distribution is normal so test statisitcs is

$z=\frac{\widehat{p}-p}{SEp}=\frac{0.51-0.5}{\sqrt{\frac{0.5*0.5}{1000}}}=0.633$

d. As alternative hypothesis is having > sign so P value is $P(z>0.633)=0.2634$

e. As P value is greater than alpha=0.05, hence we fail to reject the null hypothesis

Hence we do not sufficient evidence to support the claim that more than half of the people in the US support the idea that AI will diminsh the need for repeating tasks