Question

a sociologist claims the probability that a person picked at andom in times square new york city is visiting the area is 0.83. you think this sounds high and want to see if the balue is actually less then 0.83. you asked 50 people selected at random in times square where they are from and found 37 people who were visiting. perform the hypothesis test using a=0.05 What type of hypothesis test do you use? What is the test statistic and it’s value? What is the p value? What is your verdict? What is the reason for your verdict? At the _____ level of significance, from the sample data, there____ is/isn’t sufficient evidence to conclude that_____

Answer 1

Hypothesis test

We have to perform one sample p-test.

We have to test for null hypothesis

against the alternative hypothesis

Our test statistics is given by

Here,

Number of observations

Corresponding [Using R-code 'pnorm(-1.694197)']

Level of significance

We reject our null hypothesis if .

Here, we observe that

So, we reject our null hypothesis.

ANSWERS

We used left tailed one sample p-test.

The test statistic is z and its value is -1.694197.

The p value is 0.04511389

Our verdict is that probability that a person picked at random in times square New York city is visiting the area is lesser than 0.83.

The reason is that we found significant lesser probability in our study.

At the 0.05 level of significance, from the sample data, there is sufficient evidence to conclude that probability that a person picked at random in times square New York city is visiting the area is lesser than 0.83.