Question

A potato chip company advertises that their family sized bag of potato chips have an average weight of 10 oz. I want to know if the bags are overfilled. I randomly sampled 100 bags of chips and find that my sample has a mean weight of 10.1 oz and a standard deviation of 0.2 oz. The sample data was not strongly skewed.

1. Write the appropriate null and alternative hypothesis.

2. Calculate the t score.

3. use the t score to evaluate the strength of the evidence against the null hypothesis.

Answer 1

Here we are testing for population mean and we do not have population SD but n > 30, so we will use t-dist.

= 10.1 Sx = 0.2 n = 100

1. Write the appropriate null and alternative hypothesis.

The claim is to test whether the avg. weight is 10 oz.

(The population avg. weight is 10 oz.)

(The population avg. weight is not 10 oz.)

2. Calculate the t score.

Test Stat =

Where the null mean = 10

Test Stat = 5

3. use the t score to evaluate the strength of the evidence against the null hypothesis.

This is a two tailed test since we are testing for difference at all.

p - value = 2 P( > |Test Stat |)

= 2P( > 5)

= 2 * 0.0000

p-value = 0.000000 .............using t-dist tables

Assuming level of significance = 5%,

p-value < 0.05

We reject the null hypothesis at 5%. There is sufficient evidence to support that true weight is different from 10 oz.