Question

In a recently conducted experiment, researchers used fungi to degrade hydrocarbons, the by-products of incomplete combustion of fossil fuels. In order to be costeffective, the rate at which a particular hydrocarbon is degraded must be at least 1.00 micromole per gram of soil per minute. The researchers added fungi and growth media (essentially sugar) to the soil in 9 containers with random samples of soil and obtained the following degradation rates in micromoles per gram per minute:

0.87 | 0.91 | 1.00 |

1.08 | 1.08 | 1.09 |

1.10 | 1.23 | 1.36 |

a. Construct and interpret a 90% confidence interval for the mean degradation rate.

b.Based on this confidence interval, should the researchers be reasonably confident that this process will be cost-effective?

Answer #1

a) to construct the confidence interval of the mean we should use the t-distribution with n-1=8 degrees of freedom as the population standard deviation is not given. The 90% confidence of mean interval is given by

here the sample mean is 1.16 and the sample standard deviation is 0.2832 and the critical value for t is 1.85955. Thus the confidence interval is (1.1015, 1.2185)

b) Based on the confidence interval the researchers be reasonably confident that this process will be cost-effective as the null value 1 is not lying the confidence interval.

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