Question

A political pollster claims that 55% of voters prefer candidate A. To investigate this claim, a random sample of 75 voters is polled. The pollster finds that 39 of those polled prefer candidate A. He would like to know if the data provide convincing evidence that the true proportion of all voters who prefer candidate A is less than 55%. What are the values of the test statistic and P-value for this test

Answer 1

The null hypothesis is rejected because the probability is 0.52.

What are null hypotheses and alternative hypotheses?

In null hypotheses, there is no relationship between the two phenomena under the assumption that it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.

A political pollster claims that 55% of voters prefer candidate A.

To investigate this claim, a random sample of 75 voters is polled.

The pollster finds that 39 of those polled prefer candidate A.

He would like to know if the data provide convincing evidence that the true proportion of all voters who prefer candidate A is less than 55%.

This is left tailed test

H₀: p = 0.55

Hₐ: p < 0.55

Then the probability will be

p = 39 / 75

p = 0.52

P-value = 0.3015

Interpretation of P-value:- In a random sample of 75 voters, the chance of getting a sample statistic of 0.52 or below is 0.3015, assuming that the real population proportion of the voter base who chooses candidate A is 0.55.

More about the null hypotheses and alternative hypotheses link is given below.

brainly.com/question/9504281

#SPJ1