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patriot [66]
3 years ago
6

. The National Sleep Foundation surveyed representative samples of adults in six different countries to ask questions about slee

ping habits.† Each person in a representative sample of 250 adults in each of these countries was asked how much sleep they get on a typical work night. For the United States, the sample mean was 391 minutes, and for Mexico the sample mean was 426 minutes. Suppose that the sample standard deviations were 25 minutes for the U.S. sample and 49 minutes for the Mexico sample. The report concludes that on average, adults in the United States get less sleep on work nights than adults in Mexico. Is this a reasonable conclusion? Support your answer with an appropriate hypothesis test. (Use
= 0.05.
Use 1 for Mexico and 2 for the United States.)
Mathematics
1 answer:
scoundrel [369]3 years ago
6 0

Answer:

Yes the conclusion in the question  is a reasonable conclusion

Step-by-step explanation:

From the question we are told that

    The sample size is  n_1 = n_2 = n = 250

     The sample mean for USA is  \= x_1 =  391 \ minutes

     The sample mean for Mexico is \= x_2 = 426 \ minutes

     The sample standard deviation for USA is  s_1 =  25 \ minutes

    The sample standard deviation for Mexico is  s_2 =  49 \  minutes

     

The null hypothesis is  H_o  :  \mu_1 = \mu_2

The alternative hypothesis is  H_a  :  \mu_1  < \mu_2

Generally the test statistics is mathematically represented as

        z =  \frac{\= x_1 - \= x_2 }{ \sqrt{ \frac{s_1^2}{n_1} + \frac{s_2^2}{n_2 } } }

=>     z =  \frac{ 391  - 426  }{ \sqrt{ \frac{25^2}{250} + \frac{49^2}{250} } }

=>     z =  -10

From the z table  the area under the normal curve to the left corresponding to   -10  is

    p-value =  P(Z <  -10 ) =  0.00

Generally from the value obtained we see that

  The p-value is  <  \alpha  hence

The decision rule is

Reject the null hypothesis

The conclusion is  

 The is sufficient evidence to conclude that adults in the United States get less sleep on work nights than adults in Mexico

Hence the conclusion in the question is a  reasonable conclusion

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