For the given hypothesis test, explain the meaning of a Type I error, a Type II error, or a correct decision as specified.
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 lead to the
conclusion that µ> 0.4 ppm
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.
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 fail to lead
to rejection of that fact.
A sample mean, sample standard deviation, and sample size are given. Use the one–mean t–test to perform the required
hypothesis test about the mean, µ, of the population from which the sample was drawn. Use the critical–value approach.
x=40.9, s =6.5, n = 15, H0: µ= 32.6, Ha: µ
32.6, = 0.05.
Test statistic: t =4.95. Critical values: t = ±2.145. Do not reject H0: µ= 32.6. There is not
sufficient evidence to support the claim that the mean is different from 32.6.
Test statistic: t =4.95. Critical values: t = ±1.96. Reject H0: µ= 32.6. There is sufficient evidence
to support the claim that the mean is different from 32.6.
Test statistic: t =4.95. Critical values: t = ±2.145. Reject H0: µ= 32.6. There is sufficient
evidence to support the claim that the mean is different from 32.6.
Test statistic: t =4.95. Critical values: t = ±1.96. Do not reject H0: µ= 32.6. There is not
sufficient evidence to support the claim that the mean is different from 32.6.