A research company wants to estimate the percentage of citizens of a city who are willing to invest in real estate in the coming 2 years, and will declare that the real estate market is shrinking if this percentage is lower than 21%. In a survey among 1100 citizens, 213 of them are willing to invest within 2 years. Construct a 95% confidence interval for the proportion of the citizens of that city who are willing to invest in real estate in the coming 2 years and briefly comment on the real estate market.

The population sampleproportion is

[give an answer between 0 and 1 correct to 4 decimal places].

The critical value is [correct to 4 decimal places].

According to the formula

the confidence interval is:Answer

According to the confidence interval, although the is than [give an answer between 0 and 1 here], the research company % confident that the of citizens who are willing to invest in real estate in the coming 2 years is truly

. Therefore, the research company

declare that the real estate market in this city is shrinking.

d) The manager of a singing agency wants to know the customer spending on CD on their singers. It is believed that it is a good result if customers would spend at least an average of $1600. A random sample of 19 customers is selected. The spending data on CD (in dollars) are listed below:

8631549849176964239611962320145310757621503174815251343154215894621602

Use the given data to construct a 80% confidence interval estimate of the mean spending on CD on their singers and briefly comment and suggest on the spending of the customers on the singers.

The mean and standard deviation of the data are

and , respectively [correct to 4 decimal places].

The critical value is [correct to 4 decimal places].

According to the formula

the confidence interval is:( ) ( )

According to the confidence interval, the manager is( )

% confident that ( )spending is( )than( )

. Therefore, the mean spending of customers( )

the expectation of the company and the singing

agency( )

think of more promotion on their singers in selling CD.