You are conducting a study to see if the mean doctor's salary (in thousands of dollars) is significantly more than 86. A random sample of 26 doctors' salary in thousands of dollars is shown below. Test the claim using a 5% level of significance. Give answer to at least 4 decimal places. Salary 79.79 82.14 82.44 80.19 88.62 94.42 94.81 93.01 91.41 86.49 84.73 86.14 92.02 80.09 86.13 90.12 85.89 98.63 89.58 91.03 91.37 94.99 93.89 105.37 88.87 100.33 What are the correct hypotheses? H0: ___ thousand dollars H1: _ thousand dollars Based on the hypotheses, find the following: Test Statistic = _ Critical-value = _ Shade the sampling distribution curve with the correct critical value(s) and shade the critical regions. The arrows can only be dragged to t-scores that are accurate to 1 place after the decimal point (these values correspond to the tick marks on the horizontal axis). Select from the drop down menu to shade to the left, to the right, between or left and right of the t-score(s). Shade: . Click and drag the arrows to adjust the values. -1.5 The correct decision is to The correct summary would be: that the population mean doctor's salary (in thousands of dollars) is significantly more than 86.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

You are conducting a study to see if the mean doctor's salary (in thousands of dollars) is significantly more than 86. A random sample of 26 doctors' salary in thousands of dollars is shown below. Test the claim using a 5% level of significance. Give answer to at least 4 decimal places.

Salary
79.79
82.14
82.44
80.19
88.62
94.42
94.81
93.01
91.41
86.49
84.73
86.14
92.02
80.09
86.13
90.12
85.89
98.63
89.58
91.03
91.37
94.99
93.89
105.37
88.87
100.33

What are the correct hypotheses?

H₀: _____ thousand dollars

H₁: _____ thousand dollars

Based on the hypotheses, find the following:

Test Statistic = ___

Critical-value = ___

Shade the sampling distribution curve with the correct critical value(s) and shade the critical regions. The arrows can only be dragged to t-scores that are accurate to 1 place after the decimal point (these values correspond to the tick marks on the horizontal axis). Select from the drop down menu to shade to the left, to the right, between or left and right of the t-score(s).

Shade: . Click and drag the arrows to adjust the values.

-1.5

The correct decision is to ______

The correct summary would be: ____ that the population mean doctor's salary (in thousands of dollars) is significantly more than 86.

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 + ...

Expert Solution

Step 1

Given:

Sr. No.	Salary (x)
1	79.79
2	82.14
3	82.44
4	80.19
5	88.62
6	94.42
7	94.81
8	93.01
9	91.41
10	86.49
11	84.73
12	86.14
13	92.02
14	80.09
15	86.13
16	90.12
17	85.89
18	98.63
19	89.58
20	91.03
21	91.37
22	94.99
23	93.89
24	105.37
25	88.87
26	100.33