Assume that the differences are normally distributed. Complete parts (a) through (d) below. Observation 1 2 3 4 6. 7 8 X1 42.3 47.2 43.6 46.4 47.9 45.6 48.2 49.6 Yi 45.5 46.4 45.7 50.5 50.4 45.7 49.4 49.7 (a) Determine d; = X; - Y; for each pair of data. Observation 1 3 4 6 7 8 d; (Type integers or decimals.) (b) Compute d and d = (Round to three decimal places as needed.) Sa =| (Round to three decimal places as needed.) (c) Test if Hd < 0 at the a = 0.05 level of significance. LO
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![Assume that the differences are normally distributed. Complete parts (a) through (d) below.
Observation
1
2
3
4
6.
7
8
X1
42.3
47.2
43.6
46.4
47.9
45.6
48.2
49.6
Yi
45.5
46.4
45.7
50.5
50.4
45.7
49.4
49.7
(a) Determine d; = X; - Y; for each pair of data.
Observation
1
3
4
6 7
8
d;
(Type integers or decimals.)
(b) Compute d and
d =
(Round to three decimal places as needed.)
Sa =| (Round to three decimal places as needed.)
(c) Test if Hd < 0 at the a = 0.05 level of significance.
LO](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4613800d-47f3-4159-b005-37949e212108%2F9be734d2-c193-43fa-8862-ccd27aeac81e%2Fe3j2oj.png&w=3840&q=75)
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