What is the 90% confidence interval of the mean? NarmalNo SpacingHeading 1Heading 2TitleSubtitleSubtFemalesBalance TimeExercise days per week Favorite ExerciseSwimmingSwimmingWalkingJogging130438433242335Aerobics6.7.283.JoggingSwimmingSwimming32483521. The mean and standard deviation for the time in seconds forfemales who participated:Mean = 30+ 38+32+ 23+35+28+32+ 35= 253Mean = 253/8=31.6x-meanx mean?30-1.6386.4320.423-8.6353.428-3.6320.4353.4SD = V153.88/8= 4.386= 4.4Focus

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Description: What is the 90% confidence interval of the mean? NarmalNo SpacingHeading 1Heading 2TitleSubtitleSubtFemalesBalance TimeExercise days per week Favorite ExerciseSwimmingSwimmingWalkingJogging130438433242335Aerobics6.7.283.JoggingSwimmingSwimming3248352

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What is the 90% confidence interval of the mean?

Narmal
No Spacing
Heading 1
Heading 2
Title
Subtitle
Subt
Females
Balance Time
Exercise days per week Favorite Exercise
Swimming
Swimming
Walking
Jogging
1
30
4
38
4
3
32
4
23
35
Aerobics
6.
7.
28
3.
Jogging
Swimming
Swimming
32
4
8
35
2
1. The mean and standard deviation for the time in seconds for
females who participated:
Mean = 30+ 38+32+ 23+35+28+32+ 35= 253
Mean = 253/8=31.6
x-mean
x mean?
30
-1.6
38
6.4
32
0.4
23
-8.6
35
3.4
28
-3.6
32
0.4
35
3.4
SD = V153.88/8
= 4.386
= 4.4
Focus

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Step 1

A confidence interval is an interval that has the property that is very likely that the population parameter is contained by it and this likelihood is measure by the confidence level .

The formula for a confidence interval for the population mean $μ$ when the population standard deviation is not known is

CI= $(\bar{x} - t_{α / 2, n - 1 } \times \frac{s}{\sqrt{n}} , \bar{x} + t_{α / 2, n - 1 } \times \frac{s}{\sqrt{n}})$

where the value $t_{α /2, n - 1}$ is the critical t-value associated with the specified confidence level and the number of degrees of freedom df = n -1.

Given :

The provided sample mean is $\bar{X}$ $= 31.6$ and the sample standard deviation is $s = 4.4$ . The size of the sample is $n = 8$ and the required confidence level is 90%.

The number of degrees of freedom are $d f = 8 - 1 = 7$ , and the significance level is $α = 0.1$ .

Based on the provided information, the critical t-value for $α = 0.1$ and $d f = 7$ degrees of freedom is $t_{c} = 1.895$ .

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