Question

Miller (2008) examined the energy drink consumption

of college undergraduates and found that males use

energy drinks significantly more often than females.

To further investigate this phenomenon, suppose that

a researcher selects a random sample of n = 36 male

undergraduates and a sample of n = 25 females. On

average, the males reported consuming M = 2.45

drinks per month and females had an average of

M = 1.28. Assume that the overall level of consumption

for college undergraduates averages u = 1.85

energy drinks per month, and that the distribution of

monthly consumption scores is approximately normal

with a standard deviation of (infinity sign) =  1.2.

a. Does this sample of males support the conclusion

that males consume significantly more energy

drinks than the overall population average? Use a

one-tailed test with (infinity sign) = .01.

b. Does the sample of females support the conclusion

that females consume significantly fewer energy

drinks than the overall population average? Again,

use a one-tailed test with (infinity sign).01.

Answer 1

Solution:-

Given

a) State the hypothesis and select an alpha ()level.

The null hypothesis states that males consume not significantly more energy drinks than the overall population mean.

H0 ; 1.85 (not more than 1 85)

The alternative hypothesis states that the males consumes significantly more energy drinks than the overall population mean.

H1: > 1.85 (more than t 85)

Level or significance, =0.01

Thus, there is a 1% risk of committing a Type / error If we reject H0.

Locate the critical region With a. 0.01.the critical region consists of sample means that corresponds to z-score larger Man c%cal value of z=233

Obtain the sample data, and compute the test statistics

We have,

Standard deviation, a =1.2

Sample size, n=36

For this problem, the distribution of sample means, according to the null hypothesis, will be normal with an expected value of =1.85 and a standard error of

=

=1.2 / 6
= 0.20
In this distribution, our sample mean of males M = 2.45 correspondents to a
z-score of

= 2.45 -1.85 /0.2

= 0.6 /0.2

3.00

Make a decision about H„, and state the conclusion

The z-score we obtained is in the critical region This indicates that our sample mean of M = 2.45 is extreme to be obtained from a population with =1.85

Therefore, our statistical decision is to reject H, Our conclusion for the study is that the data the data provide sufficient evidence that the males consume significantly more energy drinks than the overall population average
b) State the hypothesis and select an alpha ( a)level.

The null hypothesis states that females consume not significantly fewer energy drinks than the overall population mean.

H0 : 1.85 (net less than 1 85)

The alternative hypothesis Mates that the males consumes significantly more energy drinks than the overall population mean H, : <1.85 (less than 1 85)

Level of significance, a = 0.01

Thus, there is a 146 risk of committing a Type I error if we reject H0.

Locate the critical region.

With = 0.01, the critical region consists of sample means that corresponds to z-score smaller than the critical value of z = -2.33

Obtain the sample data and compute the test statistics.

We have ,

Standard deviation =1.2

Sample size , n = 25

For this problem , the distribution of sample means , according to the null hypothesis , will be normal with an expected value of =1.85 and a standard error of

=

= 1.2 /5

= 0.24

In this distribution, our sample mean of females M =1.28 corresponds to a z- score of

=1.28 -1.85 / 0.24

= -0.57 /0.24

= -2.375

Make a decision about H0 ,and state the conclusion.

The z-score we obtained is an critical region. This includes that our sample mean of M = 1.28 IS is example to be obtained from a population with = 1.85 .

Therefore ,our statistical decision is to reject H0

Our conclusion for the study is that the data the data provide sufficient evidence that the females consume significantly fewer energy drinks than the overall population average.

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