1. The sales manager of a food company wants to determine if the weekly sales of
ID: 3318108 • Letter: 1
Question
1. The sales manager of a food company wants to determine if the weekly sales of 16 ounce packages of frozen broccoli has increased since last year. The mean weekly number of sales per store was 2,400 packages last year. The sales manager set the following hypotheses to test
Available sales data are from 400 stores. Assume that this data set is a random sample. The sample mean is 2,460 and the sample standard deviation is 800. For the significance level of 1%, find the critical value.
2503.2
2296.8
2493.2
2460
2306.8
2.
The production manager of a manufacturer wants to evaluate a modified ball bearing production process. When the process is operating properly, the process produces ball bearings whose weights have a mean of 5 ounces and a standard deviation of 0.1 ounce. A new raw-material supplier was used for a recent production run, and the manager wants to know if that change has caused any problem. If there was a problem, the mean weight of a ball bearing would be different.
The manager will test the following hypotheses
From a random sample of 100 ball bearings, the sample mean was 4.98. The significance level is specified as 10%. What is the probability of type I errors in this hypothesis testing?
0.02%
4.98%
2.58%
10.00%
5.00%
3. The manufacturer of a new compact car claims that the car will average at least 35 miles per gallon in general highway driving.
For 100 test runs, the car averaged 35.5 miles per gallon with a standard deviation of 4 miles per gallon.
Suppose that the manufacturer tests the following hypotheses:
Consider the 10% significance level. What is the power of the test if the actual average fuel efficiency is 36 miles per gallon?
56.749%
99.086%
88.877%
80.511%
95.254%
4.
A government agency receives many consumer complaints that the boxes of detergent sold by a company contain less than the 20 oz of detergent advertised.
To check the consumers' complaints, the agency purchases 100 boxes of the detergent and finds that the sample mean is 19.3 oz and the sample standard deviation is 4 oz.
The agency conducts a testing of the following hypotheses at the 1% level of significance:
What is the p-value and the result of the hypothesis testing?
The p- value is 4.006%, so the null hypothesis is rejected.
The p- value is 6.681%, so the null hypothesis is rejected.
The p- value is 6.681%, so the null hypothesis is not rejected.
The p- value is 4.006%, so the null hypothesis is not rejected.
The p- value is 10.565%, so the null hypothesis is not rejected.
The p- value is 10.565%, so the null hypothesis is rejected.
5.
The manager of a firm wants to determine if the average hourly wage for semi-skilled workers is $9 in the Capital District.
In order to do so, she takes a random sample of 100 hourly wages and finds that the sample mean is $8 and the sample standard deviation is $2.
The hypotheses to be tested are:
Assume that the actual average is $8.8. What is the probability of type II error at the 10% significance level?
85.668%
94.277%
92.091%
82.993%
73.477%
a.2503.2
b.2296.8
c.2493.2
d.2460
e.2306.8
Explanation / Answer
1)for 1% level and right tail ; critical z =2.33
critical value=mean +z*std deviaiton/(n)1/2 =2400+2.33*800/(400)1/2 =2493.2
2) option d 10%
3)
critical value=mean +z*std deviaiton/(n)1/2 =35.5+1.28*4/(100)1/2 =35.5126
hence Power =P(X>35.5126)=P(Z>(35.5126-36)/0.4)=P(Z>-1.2185)=0.8887
option C
4)
test statistic z =(19.3-20)/(4/(100)1/2)=-1.75
for which p value =0.04
The p- value is 4.006%, so the null hypothesis is rejected
5)for 10% critical value of z =1.645
critical region = 9-/+ 1.645*2/(100)1/2 =8.671 ; 9.329
tehrefore probability of type II error =P(8.671<X<9.329)=P((8.671-8.8)/0.2<Z<(9.329-8.8)/0.2)
=P(-0.6449<Z<2.6448)=0.9959-0.2595 ~=0.7348
73.477%
a.The p- value is 4.006%, so the null hypothesis is rejected
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