Question

Two owners of a cattle ranch, Jo and Val, want to find the average weight for the ranch's 200 cows. Instead of weighing all of the cows: Jo weighs 25 cows and gets an average weight of 1,350 pounds (stdev 50) Val weighs 100 cows and gets an average weight of 1,420 pounds (stdev 50) What is Jo's margin of error, rounded to the nearest whole number? (The formula is 1.96 straight x left parenthesis StdDev right parenthesis divided by square root of straight N)

Answer 1

The value is
`E =19.6`

Explanation:

From the question we are told that

The mean of Jo cows is
`\= x_1 = 1350`

The standard deviation of Jo cow is
`s_1 =  50`

The mean of Val cows is
`\= x_2  = 1420`

The standard deviation of Val cows is
`s_2 =  50`

The sample size for both Val and Jo is n = 25

Let assume that the level of significance is
`\alpha = 0.05`

Generally from the normal distribution table the critical value of
`(\alpha )/(2)` is

`Z_{(\alpha )/(2) } =  1.96`

Generally the margin of error is mathematically represented as

`E = Z_{(\alpha )/(2) } *  (\sigma )/(√(n) )`

Hence margin of error for Jo is

=>
`E = 1.96 *  (50)/(√(25) )`

=>
`E =19.6`