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SIZIF [17.4K]
3 years ago
13

For a set of data, x is the explanatory variable. Its mean is 8.2, and its standard deviation is 1.92. For the same set of data,

y is the response variable. Its mean is 13.8, and its standard deviation is 3.03. The correlation was found to be 0.223.
Select the correct slope and y-intercept for the least-squares line.
a. Slope = -0.35
y-intercept = -10.9
b. Slope = -0.35
y-intercept = 10.9
c. Slope = 0.35
y-intercept = -10.9
d. Slope = 0.35
y-intercept = 10.9
Mathematics
1 answer:
aniked [119]3 years ago
4 0

Answer:

d. Slope = 0.35

y-intercept = 10.9

Step-by-step explanation:

The computation is shown below:

Data given in the question

Mean \bar X = 8.2

The standard deviation  of x = \sigma = 1.92

Mean \bar Y = 13.8

The standard deviation  of y = \sigma = 3.03

The correlation = r = 0.223

Based on the above information,

As we know that

The slope is

b = r \frac{\sigma y }{\sigma x} \\\\ = (0.223) (\frac{3.03}{1.92} \\\\ = (0.223) (1.578125)

= 0.3519

Now the y-intercept is

a = \bar Y - b \bar X \\\\

= 13.8  - (0.351922) 8.2

= 13.8 - 2.88579

= 10.91

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the sample mean foot length of a simple random sample of 25 third-graders is 22.5 cm. The standard error of the mean is 0.8 cm.
GenaCL600 [577]

Question:

The sample mean foot length of a simple random sample of 25 third-graders is 22.5 cm. The standard error of the mean is 0.8 cm. Which one of the following is a correct interpretation for the standard error of the mean?

The typical distance between each individual foot length in the sample and the sample mean foot length is approximately 0.8 cm.

The typical distance between one sample mean foot length and another sample mean foot length is 0.8 cm.

The typical distance between each individual foot length in the population and the true mean foot length is approximately 0.8 cm.

The typical distance between means of samples of size 25 and the population mean foot length is approximately 0.8 cm

The typical distance between each individual foot length in the sample and the true mean foot length is approximately 0.8 cm.

Answer:

The correct option is:

The typical distance between means of samples of size 25 and the population mean foot length is approximately 0.8 cm

Step-by-step explanation:

The standard error of the mean is a measure of the extent of variation of the mean in a sample of data from that of the value of the mean within the general population. It is a statistical measure of the probability that the size of a particular sample will approach that of the population mean, with reference to the principle of the central limit theorem.

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