The final grades of forty students were randomly selected, recorded and inputted into MINITAB. The results are summarized in Exhibit 1 below. One-Sample Z: Grade Test of mu = 85 vs ≠ 85 The assumed standard deviation = 5.25 Variable N Mean StDev SE Mean Grade 40 87 5.25 * i. Calculate the value of *?  ii. State the null and alternative hypotheses for the test.  iii. What is the value of test statistic for this test.?

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a) The final grades of forty students were randomly selected, recorded and inputted into
MINITAB. The results are summarized in Exhibit 1 below.
One-Sample Z: Grade
Test of mu = 85 vs ≠ 85
The assumed standard deviation = 5.25

Variable N Mean StDev SE Mean
Grade 40 87 5.25 *
i. Calculate the value of *? 
ii. State the null and alternative hypotheses for the test. 
iii. What is the value of test statistic for this test.? 
iv. Calculate the p-value for this test. 
v. State the conclusion of this test at the 1 % level of significance. Give a reason for your
answer. 
b) A machine fills cans with soft drinks so that their contents have a volume of 330ml. Over
a period of time, it has been established that the volume of liquid in the cans follow a
normal distribution with mean of 335 ml and standard deviation of 3 ml.
A setting on the machine is altered, following which the operator suspects that themean
volume of liquid discharged by the machine into the cans has decreased. He takes a
random sample of 50 cans and finds that the mean volume of liquid in these cans is 334.6
ml. Does this confirm his suspicion? Test at the 5% level of significance. 

a) The final grades of forty students were randomly selected, recorded and inputted into
MINITAB. The results are summarized in Exhibit 1 below.
One-Sample Z: Grade
Test of mu-85 vs #85
The assumed standard deviation = 5.25
Variable
Grade
i.
ii.
iii.
iv.
V.
N
40
Mean
87
StDev
5.25
Calculate the value of *?
State the null and alternative hypotheses for the test.
What is the value of test statistic for this test.?
SE Mean
*
Calculate the p-value for this test.
State the conclusion of this test. Give a reason for your answer.
b) A machine fills cans with soft drinks so that their contents have a volume of 330ml. Over
a period of time, it has been established that the volume of liquid in the cans follow a
normal distribution with mean of 335 ml and standard deviation of 3 ml.
A setting on the machine is altered, following which the operator suspects that the mean
volume of liquid discharged by the machine into the cans has decreased. He takes a random
sample of 50 cans and finds that the mean volume of liquid in these cans is 344.6 ml. Docs
this confirm his suspicion? Test at the 5% level of significance.
Transcribed Image Text:a) The final grades of forty students were randomly selected, recorded and inputted into MINITAB. The results are summarized in Exhibit 1 below. One-Sample Z: Grade Test of mu-85 vs #85 The assumed standard deviation = 5.25 Variable Grade i. ii. iii. iv. V. N 40 Mean 87 StDev 5.25 Calculate the value of *? State the null and alternative hypotheses for the test. What is the value of test statistic for this test.? SE Mean * Calculate the p-value for this test. State the conclusion of this test. Give a reason for your answer. b) A machine fills cans with soft drinks so that their contents have a volume of 330ml. Over a period of time, it has been established that the volume of liquid in the cans follow a normal distribution with mean of 335 ml and standard deviation of 3 ml. A setting on the machine is altered, following which the operator suspects that the mean volume of liquid discharged by the machine into the cans has decreased. He takes a random sample of 50 cans and finds that the mean volume of liquid in these cans is 344.6 ml. Docs this confirm his suspicion? Test at the 5% level of significance.
Expert Solution
Step 1

As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted....

Given that

Population mean (µ)=85 

Sample size (n)=40

Sample mean =87

Standard deviation =5.25

We have to find

a..SE mean 

b..Null and Alternative hypothesis

c..test statistic

 

steps

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