In: Math

One hundred blood samples were taken from 100 individuals. All of the blood samples were run through two machines to determine if the machines were testing samples appropriately. We expect that both machines should yield similar results. Below are the results of the analysis. Assume there are 100 sample and they are normal. Are the two machines similar? Should we check into whether one machine should be replaced? Show all of your work.

Beckman Machine |
Coulter Machine |

3. |
4. |

5. | 6. |

7. | 8. |

9. | 10. |

11. | 12. |

13. | 14. |

15. | 16. |

We use two sample t test. The samples are normally distributed. A two sample t test is used to determineif the means of two groups differ significantly. Here two groups are two machines.

We use minitab to solve the problem.

Steps : stat, basic statistics, two sample-t test.

conclusion : as p-value =0.673 >0.05 we accept the null hypothesis and conclude there is no significant difference in the mean i.e both machines produce similar results. So, no machine should be replaced.

Nine samples were taken from 2 streams, four from one and five
from the other and the following data were obtained.
Pollution lever in stream 1: ppm
Pollution level in stream 2: ppm
16
9
12
10
14
8
11
6
Someone claimed that the data proved that stream 2 is less
polluted than stream 1.
Someone else asked the following questions: When were the data
collected? Were the data collected all in one day or on different
days? Were...

Two random samples were drawn from members of the U.S. Congress.
One sample was taken from members who are Democrats and the other
from members who are Republicans. For each sample, the number of
dollars spent on federal projects in each congressperson's home
district was recorded. Dollars Spent on Federal Projects in Home
Districts Party Less than 5 Billion 5 to 10 Billion More than 10
billion Row Total Democratic 6 16 23 45 Republican 11 17 19 47
Column...

Two random samples were drawn from members of the U.S. Congress.
One sample was taken from members who are Democrats and the other
from members who are Republicans. For each sample, the number of
dollars spent on federal projects in each congressperson's home
district was recorded. Dollars Spent on Federal Projects in Home
Districts Party Less than 5 Billion 5 to 10 Billion More than 10
billion Row Total Democratic 9 11 25 45 Republican 11 19 17 47
Column...

Twenty samples with 100 units each were taken; with the
following number of defectives in each respective sample: 11, 2, 7,
5, 6, 7, 8, 5, 3, 6, 4, 3, 5, 6, 2, 5, 0, 9, 10, and 8.
Calculate the center line, upper control limit, and lower
control limit for a 3s p-chart. (RE: As your starting
point, recall that p-charts represent percentages
of defects for samples.)
Plot the points on the chart.
Comment on whether the process is...

One hundred students were given an Algebra test. A random sample
of ten students was taken out of class of 800 enrolled students.
The time it took each student to complete the test is recorded
below.
22.2, 23.7, 16.8, 18.3, 19.7, 16.9, 17.2, 18.5, 21.0, and
19.7
a. Find the mean, variance and standard deviation for this
sample of ten students
b. Construct a 95% confidence interval for the population mean
time to complete this Algebra test.
c. Test if...

One hundred men and 100 women were asked to try a new toothpaste
and to state whether they liked or did not like the new taste
thirty-two and 26 women said they did not like the new taste does
this indicate a difference in preferences between men and women in
general?

male
1st Systolic
1st Diastolic
2nd Systolic
2nd Diastolic
1
132
74
132
82
2
108
70
108
74
3
124
78
134
78
4
116
42
116
48
5
118
76
116
70
6
128
80
128
80
7
132
90
130
92
8
106
64
110
64
female
1
168
46
156
52
2
198
82
192
84
3
110
74
110
76
4
170
94
168
100
5
142
58
140
52
6
168
52
172
54...

1.Water samples were taken from water used for cooling as it was
being discharged from a power plant into a river. It has been
determined that as long as the mean temperature of the discharged
water is at most 150 F, there will be no negative impact on the
river's ecosystem. To investigate whether a plant is in compliance
with regulations that prohibit a mean discharge water temperature
above 150 F, researchers took 50 water samples at randomly selected
times...

For all possible samples of 18 values taken from a population
with a mean of −36.33 and a standard deviation of 15.26
P(X(mean) > -33.38)=?

Two random samples are taken, one from among UVA students and the other from among UNC students. Both groups are asked if academics are their top priority. A summary of the sample sizes and proportions of each group answering yes" are given below: UVA (Pop. 1): n1 = 89,\(\hat{p}_{1}\)
= 0.81 UNC (Pop. 2): n2 = 86,\(\hat{p}_{2}\) = 0.561 Find a 97.3% confidence interval for the difference P1 – P2 of the population proportions. Confidence interval = _______

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