Question

Think of a problem that you may be interested in that deals with a comparison of two population means. Propose either a confidence interval or a hypothesis test question that compares these two means. Gather appropriate data and post your problem

For example, you may want to know if the average weight of a rippled potato chip is the same as the average weight of a non-rippled potato chip. You may weigh rippled regular potato chips from a large bag and find weights of 1.7, 1.9, 2.4, 1.3, 1.7, and 2.0 grams. You may weigh non-rippled potato chips from another large bag and find weights of 1.8, 1.6, 1.9, 1.9, and 1.4 grams. Assume a random sample was drawn.

Answer 1

In order to solve this question I used R software.

R codes and output:

> x=c(1.7,1.9,2.4,1.3,1.7,2)
> y=c(1.8,1.6,1.9,1.9,1.4)
> var(x)
[1] 0.1346667
> var(y)
[1] 0.047
> sd(x)
[1] 0.3669696
> sd(y)
[1] 0.2167948
> t.test(x,y)

Welch Two Sample t-test

data: x and y
t = 0.6351, df = 8.2552, p-value = 0.5426
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.2959699 0.5226366
sample estimates:
mean of x mean of y
1.833333 1.720000

Hypothesis:

First we check the variance of two data sets. Variances are not equal. Hence we use Welch T test statistic.

Test statistic = 0.6351

p-value = 0.5426

Since p-value is greater than 0.05, we accept null hypothesis at 5% level of significance and conclude that average weight of rippled potato chips and non-rippled potato chips is same.