Mathematics: 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).

where is this problem from?Step-by-step explanation:...

In a population, 11% of people are left handed.

blackopsty23

21.01.2022

The sample proportion p = 0.10

The claimed proportion p0 = 11%

Step-by-step 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 $H_{1} = P_{0} \neq 0.11$

Step 2:-

the test statistic

$Z =\frac{p-P_{0} }{\sqrt{\frac{P_{0} Q_{0} }{n } } }$

substitute all values and simplification we get

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

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.

0,0(0 оценок)