Question

A restaurant chain is measuring the levels of arsenic in chicken from its suppliers. The question is whether there is evidence that the mean level of arsenic is greater than 80 ppb. The levels of arsenic (in ppb) are:

68,75,81,93,95,134

1. What is the sample mean for the data? Use the appropriate notation.

     2.    Write the null and alternative hypothesis.

3.    Describe the meaning of the parameter used in Part (2)

4. Translate the original sample data by the appropriate amount to create a new dataset in which the null hypothesis is true. How do the sample size and standard deviation of this new dataset compare to the sample size and standard deviation of the original dataset?

5. Describe in detail how to create one randomization sample.

     6. Use StatKey to find the p-value.

     7. State your decision based on the p-value

     8. Write your conclusion in context.

     9. Could you have made a Type I error or a Type II error?

Answer 1

1. What is the sample mean for the data? Use the appropriate notation.

x = 68+75+81+93+95+134/6 = 91

     2.    Write the null and alternative hypothesis.

The hypothesis being tested is:

H₀: µ = 80 ppb

H_a: µ > 80 ppb

3.    Describe the meaning of the parameter used in Part (2)

The population mean is hypothesized to be greater than 80.

4. Translate the original sample data by the appropriate amount to create a new dataset in which the null hypothesis is true. How do the sample size and standard deviation of this new dataset compare to the sample size and standard deviation of the original dataset?

The sample size is 6 and the standard deviation is 23.469. The original data set is not provided but the sample is the representation of the population.

5. Describe in detail how to create one randomization sample.

Take the random values from the population and consider this as a sample which is a randomized sample.

     6. Use StatKey to find the p-value.

The p-value is 0.1514.

     7. State your decision based on the p-value

Since the p-value (0.1514) is greater than the significance level (0.05), we cannot reject the null hypothesis.

     8. Write your conclusion in context.

Therefore, we cannot conclude that the mean level of arsenic is greater than 80 ppb.

     9. Could you have made a Type I error or a Type II error?

A Type II error