Question

t.test(CurrentSmk1997est, Smokers 2017)

        Welch Two Sample t-test

data:  CurrentSmk1997est and Smokers2017

t = 62.221, df = 5680.6, p-value < 2.2e-16

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

 6.697684 7.133459

sample estimates:

mean of x mean of y 

 24.78818  17.87261 

Use the output above. In your own words, what was the mean smoking rate for the U.S. in 1997 and the mean rate in 2017, and are these two means statistically different or statistically the same?

Answer 1

Given output:

        Welch Two Sample t-test

data: CurrentSmk1997est and Smokers2017

t = 62.221, df = 5680.6, p-value < 2.2e-16

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

6.697684 7.133459

sample estimates:

mean of x      mean of y

24.78818     17.87261

Interpretation:

Hypothesis:

Null hypothesis H0: true difference in means is equal to 0

Alternative hypothesis H1: true difference in means is not equal to 0

The mean smoking rate for the U.S. in 1997 (mean x)= 24.78818

The mean smoking rate for the U.S. in 2017 (mean y) = 17.87261

To test the significance of the test:

To test the significance of the test we compare the p-value with given level of significance alpha.

we reject the null hypothesis if p-value < alpha.

(alpha is considered as 0.001, 0.01or 0.05, generally it is given as 0.05)

if p –value <0.05, there is significant difference.

if p –value <0.01, there is highly significant difference.

if p –value <0.001, there is very high significant difference.

Result:

Here the p-value <2.2e-16 i.e. p-value <0.001, therefore we reject the null hypothesis and accept the alternative hypothesis.

Conclusion: The true difference in means is not equal to 0. i.e. There is significant difference between the mean smoking rate for the U.S. in 1997 and the mean rate in 2017.