The province of Manitoba is interested to estimate the true proportion of people who have received the first COVID-19 vaccine.A study was conducted to address this concern. A random sample of 100 people was selected (who were eligible for the vaccine), 45 of whom said they have received the vaccine.

a) Construct a 95% confidence interval for estimating the true population proportion

(b) Provide an interpretation of the confidence interval in part (a)

Conduct an appropriate hypothesis test, at the 5% level of significance to test the claim that more than 40% of Manitobans received the vaccine. Provide the following:

(c)hypotheses statement

(d)test statistic value, please indicate type of test being used

(e)P-value

(f)conclusion