Question

Part a) Consider the population of all students at a University. Suppose that 38% of students have a Mastercard, 51% a Visa, and 24% have both types of credit cards. If a randomly selected student has a Mastercard, what is the probability they have a Visa?

a) 0.6316

b) 0.6500

c) 0.1938

d) 0.7451

e) 0.4706

Part b) Which of the following is a valid way of interpreting a p-value?

a) The p-value is the probability that we would observe sample data as extreme or more extreme in favour of the alternative hypothesis than that which was actually observed (assuming the null hypothesis is true).

b) The p-value is the probability that the sample mean equals the population mean.

c) The p-value measures the researcher's personal (subjective) probability that the null hypothesis is true.

d)  The p-value is the probability that you reject H₀ when H_ais true.

e) The p-value is a measure of how much the prior information (rather than the statistical evidence in the sample) supports the null hypothesis.

Answer 1

Part a) P(M) = P(students have mastercard) = 0.38

P(V) = P(students have Visa) =0.51

P(M V) = 0.24

If a randomly selected student has a Mastercard, the probability they have a Visa =P(M/V) = 0.24/0.38 = 0.6316

option a is true

Part b)

d)  The p-value is the probability that you reject H0 when Hais true.