1. Large oranges have a mean weight of about 200 g with a standard deviation of
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Question
1. Large oranges have a mean weight of about 200 g with a standard deviation of about 20 g and an approximate normal distribution. Each bag has 16 oranges. What is the distribution of the average weight of individual oranges?
a) N (mean=200, std dev=20)
b) N (mean=200, std dev=5)
c) N (mean=200, std dev=1.25)
d) N (mean=200, std dev=80)
2. A shipment of 10,000 bags of oranges arrives at a distribution center with a nominal weight of 3200 g per bag. A sample of 25 bags is selected and weighed. The average weight of the sample is 3300 g. From past shipments, it is known that the standard deviation of weight among cartons is 80 g. Find a 95% confidence interval for the mean weight of all the bags of oranges in the shipment.
a) 3200 ± 31.4
b) 3300 ± 31.4
c) 3300 ± 16
d) 3200 ± 16
3. A shipment of 1000 cartons of fruit arrives at a distribution center with a nominal weight of 10 lbs per carton. A sample of 20 cartons is selected and weighed. The average weight of the sample is 9.8 lbs. From past shipments, it is known that the standard deviation of weight among cartons is 2 lbs. The auditor wishes to test the hypothesis that the average weight of the cartons matches the nominal value vs. that the cartons are underweight at = 0.05. The test statistic (z-score) is:
a) –0.10
b) –0.45
c) –1.0
d) –1.65
4. In a test of statistical significance, the p-value tells us:
a) if the null hypothesis is true.
b) if the alternate hypothesis is true.
c) the largest level of significance at which the null hypothesis can be rejected.
d) the smallest level of significance at which the null hypothesis can be rejected.
5. All else being equal, which of the following is true?
a) As you increase the sample size, you will decrease the p-value.
b) As you increase the standard deviation, the level will increase.
c) As you increase the level, the p-value decreases.
d) As the sample mean gets further from the mean, the p-value will increase.
please explain so I can understand
Explanation / Answer
Ans:
1)
Mean=200
standard deviation=20/sqrt(16)=5
option b is correct.
2)
95% confidence interval of mean
=3300+/-1.96*(80/sqrt(25))
=3300+/-31.4
option b is correct.
3)
z=(9.8-10)/(2/sqrt(20))
z=-0.45
4) The p-value tells us that the smallest level of significance at which the null hypothesis can be rejected.
(as we reject null hypothesis,when p-value<alpha)
5)As you increase the sample size, you will decrease the p-value.
As,largere the sample size,larger the test statistic,so smaller the p-value.
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