A researcher is investigating a government claim that the unemployment rate is less than 5%. To test this claim, a random sample of 1500 people is taken and its determined that 92 people are unemployed. The following is the setup for this hypothesis test:

H0:p=0.05 Ha:p<0.05

Required:
Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.

Question

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Respuesta :

dfbustos dfbustos · Answer 1 · 2020-06-07T03:48:07+02:00

Answer:

[tex]\hat p=\frac{92}{1500}=0.0613[/tex] estimated proportion of unemployed

[tex]z=\frac{0.0613 -0.05}{\sqrt{\frac{0.05(1-0.05)}{1500}}}=2.01[/tex]

Step-by-step explanation:

Information given

n=1500 represent the random sample taken

X=92 represent the number of people unemployed

[tex]\hat p=\frac{92}{1500}=0.0613[/tex] estimated proportion of unemployed

[tex]p_o=0.05[/tex] is the value to value to test

z would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test if the true proportion is lower than 0.05 or no and the system of hypothesis are::

Null hypothesis:[tex]p \geq 0.5[/tex]

Alternative hypothesis:[tex]p < 0.5[/tex]

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)

Replacing the info given we got:

[tex]z=\frac{0.0613 -0.05}{\sqrt{\frac{0.05(1-0.05)}{1500}}}=2.01[/tex]