master
UNIVERSITY OF LIMPOPO
Turfloop Campus
School of Mathematical and Computer Sciences
Department of Statistics and Operations Research
F LIMPOPO
YO
UN
I VERSIT
Faculty of Science and Agriculture
1. Explain carefully the difference between each of the following pairs of terms:
a)
b)
c)
d)
e)
Null and alternative hypotheses
Simple and composite hypotheses
One-sided and two-sided alternatives
Type I and Type II errors
Significance level and power
2. During 2000 and 2001, many people in Europe objected to purchasing genetically modified food that was produced by farmers in the United States. The U.S. farmers argued that there was no scientific evidence to conclude that these products were not healthy. The Europeans argued that there still might be a problem with food.
a) State the null and alternative hypotheses from the perspective of the
Europeans.
b) State the null and alternative hypotheses from the perspective of the U.S. farmers. 3. Bank cash machine need to be stocked with enough cash to meet demand over an entire weekend. However, the bank will lose out on interest payments on any excess cash stocked into the cash machines. A particular bank believes that the mean withdrawal rate per transaction is normally distributed with a mean of $150 and a standard deviation of $50. Is there any evidence that the bank has got its calculations wrong, if a random sample of 36 customer transactions gives a mean sample of $160? State your null and alternative hypotheses.
4. A random sample is obtained from a population with variance
, and the sample mean is computed. Test the null hypothesis versus the alternative hypothesis with . compute the critical value ̅ and state your decision rule for the following options:
a) Sample size
b) Sample size
c) Sample size
d) Sample size
5. A random sample of is obtained from a population with variance , and the sample mean is computed. Test the null hypothesis versus the
People who
Turfloop Campus
School of Mathematical and Computer Sciences
Department of Statistics and Operations Research
F LIMPOPO
YO
UN
I VERSIT
Faculty of Science and Agriculture
1. Explain carefully the difference between each of the following pairs of terms:
a)
b)
c)
d)
e)
Null and alternative hypotheses
Simple and composite hypotheses
One-sided and two-sided alternatives
Type I and Type II errors
Significance level and power
2. During 2000 and 2001, many people in Europe objected to purchasing genetically modified food that was produced by farmers in the United States. The U.S. farmers argued that there was no scientific evidence to conclude that these products were not healthy. The Europeans argued that there still might be a problem with food.
a) State the null and alternative hypotheses from the perspective of the
Europeans.
b) State the null and alternative hypotheses from the perspective of the U.S. farmers. 3. Bank cash machine need to be stocked with enough cash to meet demand over an entire weekend. However, the bank will lose out on interest payments on any excess cash stocked into the cash machines. A particular bank believes that the mean withdrawal rate per transaction is normally distributed with a mean of $150 and a standard deviation of $50. Is there any evidence that the bank has got its calculations wrong, if a random sample of 36 customer transactions gives a mean sample of $160? State your null and alternative hypotheses.
4. A random sample is obtained from a population with variance
, and the sample mean is computed. Test the null hypothesis versus the alternative hypothesis with . compute the critical value ̅ and state your decision rule for the following options:
a) Sample size
b) Sample size
c) Sample size
d) Sample size
5. A random sample of is obtained from a population with variance , and the sample mean is computed. Test the null hypothesis versus the
People who