Respuesta :
We conclude that less than 30% of teen girls smoke to stay thin.
Let p be the percentage of teen girls who smoke to stay thin.
So, the Null Hypothesis,([tex]H_{0}[/tex]):
p≥ 30%
This means that at least 30% of teen girls smoke to stay thin
Alternate Hypothesis,([tex]H_{A}[/tex]) :
p < 30%
This means that less than 30% of teen girls smoke to stay thin.
The test statistics that would be used here
One sample z proportion statistics:
T.S = p' - p/ [tex]\sqrt{p'(1-p')/n}[/tex] ≈N( 0,1)
Here p'= sample percent of teen girls who smoke to stay thin = 63/ 273 = 0.231
n = number of sample of teen girls = 273
Now putting these values we have:
Test statistics = 0.231 - 0.30/ [tex]\sqrt{0.231( 1- 0.231)/ 273}[/tex]
= -2.705
So we get the value of z-test statistics as - 2.705.
As there is not provided in the question that the level of significance so we assume it to be 5%. Now at a 5% significance level, the z table gives the critical value of -1.645 for left- the tailed test.
As test statistics is less than the critical value of z that is -2.705< -1.645. So we reject our null hypothesis as will fall in reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore we get that less than 30% of teen girls smoke to stay thin.
To know more about the test statistics refer to the link given below:
https://brainly.com/question/15110538
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