State your null hypothesis with scientific notation State yo

State your null hypothesis with scientific notation.

State your alternative hypothesis with scientific notation.

Calculate SE.

Calculate CI.

Calculate Z-statistic.

Make a statistical decision: i.e., whether or not to reject the null hypothesis.

Draw your conclusion: i.e., statement regarding the parameter.

1) In a recent survey, teenagers were asked to indicate how many 20-ounce bottles of sports drinks they consume in a typical week. The descriptive statistics revealed that males consumed 9 bottles on average and that females consumed 7.5 bottles of sport drinks on average. The respective SDs were 2.1 and 1.2. Both samples were of size 100. Do male teens and female teens drink the same amount of sports drinks? Test the hypothesis at the 1% level of significance.

Solution

State your null hypothesis with scientific notation.

Let mu1 be the mean for male

Let mu2 be the mean for female

Null hypothesis: mu1=mu2

---------------------------------------------------------------------------------------------

State your alternative hypothesis with scientific notation.

Alternative hypothesis: mu1 not equal to mu2

---------------------------------------------------------------------------------------------

Calculate SE.

SE= sqrt(s1^2/n1+s2^2/n2)

=sqrt(2.1^2/100+1.2^2/100)

=0.2418677

---------------------------------------------------------------------------------------------

Calculate CI.

Given a=0.01, Z(0.005) = 2.58 (from standard normal table)

So the lower bound is

(xbar1-xbar2) - Z*sqrt(s1^2/n1+s2^2/n2)

=(9-7.5) - 2.58*0.2418677

=0.8759813

So the upper bound is

(xbar1-xbar2) + Z*sqrt(s1^2/n1+s2^2/n2)

=(9-7.5) + 2.58*0.2418677

=2.124019

---------------------------------------------------------------------------------------------

Calculate Z-statistic.

Z=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)

=(9-7.5)/0.2418677

=6.20

---------------------------------------------------------------------------------------------

Make a statistical decision: i.e., whether or not to reject the null hypothesis.

Since the interval does not include 0, we reject the null hypothesis.

---------------------------------------------------------------------------------------------

Draw your conclusion: i.e., statement regarding the parameter.

So we can not conclude that mu1=mu2