Question

The first day of baseball comes in late March, ending in October with the World Series. Does fan support grow as the season goes on? Two polls, one conducted in March and one in November, both involved random samples of 1,001 adults aged 18 and older. In the March sample, 44% of the adults claimed to be fans of professional baseball, while 52% of the adults in the November sample claimed to be fans. (a) Construct a 99% confidence interval for the difference in the proportion of adults who claim to be fans in March versus November. (Let p1 be the proportion of people who claim to be baseball fans in March and p2 be the proportion of people who claim to be baseball fans in November. Use p1 − p2. Round your answers to three decimal places.)

Answer 1

Explanation:

Hello!

You need to create a 99% confidence interval for the difference of proportions between fans of baseball polled in March and November.

The parameter to estimate with the interval is ρ₁-ρ₂

Sample 1 (March)

n₁= 1001 adults aged 18 and older.

sample proportion ^ρ₁= 0.44

Sample 2 (November)

n₂= 1001 adults aged 18 and older.

sample proportion ^ρ₂= 0.52

This interval is constructed under a Z distribution, so you need to look in the Z-table for the statistic value:

`Z_(1-\alpha/2)` =
`Z_(0.995)` = 2.58

The formula for the interval is:

[(^ρ₁-^ρ₂)±
`Z_(1-\alpha/2)`*√^ρ₁(1-^ρ₁) + ^ρ₂(1-^ρ₂)]

n₁ n₂

[(0.44-0.52)±2.58*√0.44*0.56 + 0.52*0.48]

1001 1001

[-0.137;-0.023]

Note: Although proportions take numbers from 0 to 1, keep in mind that this interval was constructed for the difference between two proportions, it's all right to have a negative interval, which means that the proportion of baseball fans in November is significantly bigger.

I hope you have a SUPER day!