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In: Statistics and Probability

all hypothesis testing problems must include specification of the null and alternative hypotheses and must report...

all hypothesis testing problems must include specification of the null and alternative hypotheses and must report the p-value of the data
Standards for automated filling of bulk coffee bean bags require that the mean fill amount should be 10 kg and the s.d. of fill amounts should be no more than 0.01 kg. A random sample of 30 bags was weighed and their weights are given
10.0072
10.0021
10.0105
10.0098
10.0162
9.9756
10.0196
10.0237
10.0432
10.0147
10.053
9.9728
10.0338
9.9446
9.9959
10.0138
10.0019
10.0277
10.0108
10.0462
10.0363
10.0009
9.9761
9.9991
9.9943
10.0134
10.0326
9.9638
9.9973
9.9978
a) Use this data to determine if the mean fill amount differs from 10 at the 5% level of significance. Are the assumptions for this test reasonable? 
b) What is the probability this test would show a difference if the mean fill amount is 10.01, assuming that the s.d. is no more than 0.015. 
c) What sample size would be required to show a difference with probability 0.90 if the mean fill amount is 9.95 assuming that the s.d. is no more than 0.015.? Use 5% level of significance. 
d) Construct a 95% confidence interval for the s.d. of fill amounts.

Solutions

Expert Solution

The sample mean is :

(a)

(b)

Here we need to calculate the power of the test.

(c)

d)

Following is the output of descriptive statistics:

Descriptive statistics
X
count 30
mean 10.007823
sample standard deviation 0.024768
sample variance 0.000613
minimum 9.9446
maximum 10.053
range 0.1084

orchestra answered 2 years ago
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