Given the following null and alternative hypotheses

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.

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