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a popular weekly magazine asserts that fewer than 40% of households in the united states have changed their lifestyles because of escalating gas prices. a recent survey of 180 households finds that 67 households have made lifestyle changes due to escalating gas prices.the standard error of p(bar) is:the value of the test statistic is:the pvalue is:at a=0.10 and using the p-valuein light of your conclusion, what test error may happen?

Respuesta :

Answer: The null hypothesis is not rejected.

Step-by-step explanation:

Since we have given that

n = 180

x = 67

So, [tex]\hat{p}=\dfrac{x}{n}=\dfrac{67}{180}=0.372[/tex]

Hypothesis :

[tex]H_0:\hat{p}\geq 0.4\\\\H_1:\hat{p}<0.4[/tex]

So, test statistic value would be

[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.372-0.4}{\sqrt{\dfrac{0.4\times 0.6}{180}}}\\\\z=\dfrac{-0.027}{0.03645}\\\\z=-0.741[/tex]

At 0.01 level of significance, z = -1.28

So, -1.28<-0.741

So, we will not reject the null hypothesis as p - value = 0.2234.

Hence, the null hypothesis is not rejected.

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