Question

In a population, 11% of people are left handed. In a simple random sample of 160 people selected from this population, the proportion of left handers is 0.10. Denote the sample proportion (phat) and the claimed proportion (p0).

Answer 1

The sample proportion p = 0.10

The claimed proportion p0 = 11%

Explanation:

Step:-1

Given the claimed proportion
`P_(0)` = 11% = 0.11

`Q_(0) = 1-P_(0) = 1-0.11 = 0.89`

The sample proportion of left handers is p = 0.10

The null hypothesis
`H_(0) = P_(0) = 0.11`

The alternative hypothesis
`H_(1) = P_(0) \\eq 0.11`

Step 2:-

the test statistic

`Z =\frac{p-P_(0) }{\sqrt{(P_(0) Q_(0) )/(n ) } }`

substitute all values and simplification we get

`Z =\frac{0.10-0.11 }{\sqrt{(0.11(0.89) )/(160 ) } }`

After calculation we get

Z = -4.04

since modulus Z = 4.04 > 1.96 (tabulated value at 5% level)

we reject the null hypothesis is rejected at 5% level of significance

Conclusion:-

the claim proportion is not correct.