Question

The maximum acceptable level of a certain toxic chemical in vegetables has been set at 0.4 parts per million (ppm). A consumer health group measured the level of the chemical in a random sample of tomatoes obtained from one producer to determine whether the mean level of the chemical in these tomatoes exceeds the recommended limit. The hypotheses are H0: μ ≤ 0.4 ppm Ha: μ > 0.4 ppm where μ is the mean level of the chemical in tomatoes from this producer. Explain the meaning of a Type I error. A Type I error would occur if, in fact, μ > 0.4 ppm, but the results of the sampling fail to lead to that conclusion. A Type I error would occur if, in fact, μ ≤ 0.4 ppm, but the results of the sampling lead to the conclusion that μ > 0.4 ppm A Type I error would occur if, in fact, μ ≤ 0.4 ppm, but the results of the sampling fail to lead to rejection of that fact. A Type I error would occur if, in fact, μ > 0.4 ppm, and the results of the sampling lead to rejection of the null hypothesis that μ ≤ 0.4 ppm.

Answer 1

Answer:

Null hypothesis : $\mu \leq 0.4$

Alternative hypothesis: $\mu >0.4$

And for this case a type of error I for this case would be reject the null hypothesis that the population mean is lower or equal than 0.4 when actually is true.

A Type I error would occur if, in fact, μ ≤ 0.4 ppm, but the results of the sampling lead to the conclusion that μ > 0.4 ppm

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".  

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".  

Type I error, also known as a “false positive” is the error of rejecting a null  hypothesis when it is actually true. Can be interpreted as the error of no reject an  alternative hypothesis when the results can be  attributed not to the reality.  

Type II error, also known as a "false negative" is the error of not rejecting a null  hypothesis when the alternative hypothesis is the true. Can be interpreted as the error of failing to accept an alternative hypothesis when we don't have enough statistical power

Solution to the problem

For this case we are trying to check the following hypothesis:

Null hypothesis : $\mu \leq 0.4$

Alternative hypothesis: $\mu >0.4$

And for this case a type of error I for this case would be reject the null hypothesis that the population mean is lower or equal than 0.4 when actually is true.

A Type I error would occur if, in fact, μ ≤ 0.4 ppm, but the results of the sampling lead to the conclusion that μ > 0.4 ppm