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The number of AstraZeneca Covid-19 vaccine recipients who had severe discomfort symptoms
found to be 15 per 1000 population. Assuming the number of people who received the
AstraZeneca Covid-19 vaccine had severe discomfort symptoms follows a Poisson distribution.
Find the probability that in a randomly selected 200 population, there are 4 or 5 people
who received the AstraZeneca Covid-19 vaccine have severe discomfort symptoms.
In one company, two machines producing tire material intended for commercial airplane tires are subjected to resistance abrasion test in the field application. The QC engineer conducted their regular inspection of the two machines’ outputs. Upon test, the following data was recovered from the 29 selected samples. For Machine 1, the sample average and standard deviation was recorded to be 20mg per 1000 cycles and 2mg per 1000 cycles. For Machine 2, the sample average and standard deviation is 15mg and 8mg per 1000 cycles. Do the data support the claim that the two machines produce material with the same mean wear? Use α =0.10, and assume that each population is normally distributed but that their variances are equal.
One company produces premium grade carbon steel for Katana Sword manufacturers. Two different analytical methods were used to detect the contamination level of the carbon steel in 8 random specimens
SPECIMEN
Subjects 12345678
Method 1 1.2 1.3 1.5 1.4 1.7 1.8 1.4 1.3 Method 2 1.4 1.7 1.5 1.3 2.0 2.1 1.7 1.6
Is there sufficient evidence to conclude that tests differ in the mean contamination level use? 𝛼 = 0.01?
A milk processing company test implemented a plant-wide energy conservation program with a goal of reducing the mean daily consumption rate of at least 1,000 kWh from its normal operating plants. The conservation program was implemented in Plant B. The following data was collected on weekdays where consumption level is at its peak. Were the conservation efforts effective in achieving its goal? Compare the results with Plant A’s data where the program is not implemented using 𝛼 = 0.05. Assume that the population variances are not equal.
Plant A (kWh) 3,952.80 3,276.00 3,636.00 3,636.00 3,636.00 3,636.00 4,068.00 4,068.00 4,362.00 4,362.00 4,362.00 4,362.00 3,882.00 3,808.80 3,808.80
Plant B (kWh) 4,036.00 4,036.00 4,036.00 3,264.00 864.00 1,368.00 2,196.00 4,392.00 5,220.00 3,600.00 3,960.00 4,428.00 756.00 612.00 684.00
Two machines are used for filling plastic bottles with a net volume of 16.0 ounces. The fill volume can be assumed normal, with standard deviation 𝜎! = 0.020 and 𝜎" = 0.025 ounces. A member of the quality engineering staff suspects that both machines fill to the same mean net volume, whether or not this volume is 16.0 ounces. A random sample of 10 bottles is taken from the output of each machine. Use 𝛼 = 0.10
Machine 1 16.67 16.29 16.87 16.51 15.92 16.54
16.29 15.88
15.43 16.99
16.19 15.49
16.49 16.09
Machine 2
15.46 16.04 15.56 16.78 16.39 16.91
The strength of concrete depends, to some extent, on the method used for drying. Two different drying methods showed the following results for independently tested specimens (measurements in psi): Do the methods appear to produce concrete with different mean strengths? Use 𝛼 = 0.05 .
MethodI 𝑛! =37 𝑥̅! =3.25 𝑠! =2.10 MethodII 𝑛" =40 𝑥̅" =3.24 𝑠" =1.90
a.
Reject H0 because the data are sufficiently unusual if the null hypothesis were true
b.
Fail to reject H0 because the data are not sufficiently unusual if the null hypothesis were false
c.
Fail to reject H0 because the data are not sufficiently unusual if the null hypothesis were true
d.
Reject H0 because the data are sufficiently unusual if the null hypothesis were false
US airlines average about 4.5 fatalities per month. Assume that the probability distribution for 𝑥, the number of fatalities per month, can be approximated by a Poisson probability distribution.
What is the probability that no fatalities will occur during any given month (calculate by hand and confirm the answer using MS Excel ‘POISSONDIST’ function)?
Calculate the expected value and standard deviation of the fatalities per month.
To gauge their fear of going to a dentist, a random sample of adults completed the Modified Dental Anxiety Scale (MADA) questionnaire. Scores on a scale range from zero (no anxiety) to 25 (extreme anxiety). The mean score was 11 and the standard deviation was 4, i.e. a normal distribution with 𝜇=11 and 𝜎=4. Find the probability that someone scores between 10 and 15 on the MADA (by hand and using MS Excel).
Find the probability that someone scores above 20 on the MADA
how many ways can 4 baseball players and 4 basketball players be selected from 15 baseball players and 9 basketball players?
