Let p1 represent the population proportion of U. S. Senate and Congress (House of Representatives) democrats who are in favor of a new modest tax on "junk food". Let p2 represent the population proportion of U. S. Senate and Congress (House of Representatives) republicans who are in favor of a new modest tax on "junk food". Out of the 265 democratic senators and congressman 106 of them are in favor of a "junk food" tax. Out of the 275 republican senators and congressman only 57 of them are in favor of a "junk food" tax. Find a 95 percent confidence interval for the difference between proportions l and 2.

95 percent confidence interval for the difference between proportions l and 2 is [0.114 , 0.266].

Step-by-step explanation:

We are given that out of the 265 democratic senators and congressman 106 of them are in favor of a "junk food" tax. Out of the 275 republican senators and congressman only 57 of them are in favor of a "junk food" tax.

Firstly, the pivotal quantity for 95% confidence interval for the difference between population proportion is given by;

                        P.Q. =  ~ N(0,1)

where, = sample proportion of democratic senators and congressman who are in favor of a "junk food" tax = = 0.40

= sample proportion of republican senators and congressman who are in favor of a "junk food" tax = = 0.21

= sample of democratic senators and congressman = 265

= sample of republican senators and congressman = 275

= population proportion of U.S. Senate and Congress democrats who are in favor of a new modest tax on "junk food"

= population proportion of U.S. Senate and Congress republicans who are in favor of a new modest tax on "junk food"

Here for constructing 95% confidence interval we have used Two-sample z proportion statistics.

So, 95% confidence interval for the difference between population population, () is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                     of significance are -1.96 & 1.96}  

P(-1.96 < < 1.96) = 0.95

P( < < ) = 0.95

P( < < ) = 0.95

95% confidence interval for = [ , ]

= [ ,]

= [0.114 , 0.266]

Therefore, 95% confidence interval for the difference between proportions l and 2 is [0.114 , 0.266].

b. astronomers