A random sample of 900 people in the UK were asked to respond to this statement: the countrys future economy is positive Of these sample people, 594 agreed with the statement.

Q.A random sample of 900 people in the UK were asked to respond to this statement: “the country’s future economy is positive”. Of these sample people, 594 agreed with the statement. When the same statement is was presented to a random sample of 900 people in the US, 540 agreed with the statement.

a) Using a 1% significance level, perform a hypothesis test to determine if the proportion of people in the UK who agreed with the statement is different from that of the US

b) Determine the p-value

Q2: Given the following null and alternative hypotheses

H : σ 2 ≤ σ 2

0 1 2

H : σ 2 > σ 2

1 1

and the following sample information

Test the hypothesis at 5% level of significance and indicate whether the null hypothesis should be rejected.