You wish to test the following claim (Ha) at a significance level of a = 0.005.87.7Ha:µ + 87.7You believe the population is normally distributed, but you do not know the standard deviation.data98.2101.289.290.196.6100.7a. What is the test statistic for this sample?test statistic =Round to 3 decimal placesb. What is the p-value for this sample?p-value =Round to 4 decimal places.c. The p-value is...O less than (or equal to) agreater than ad. This test statistic leads to a decision to...O reject the nullO accept the nullO fail to reject the nulle. As such, the final conclusion is that...O There is sufficient evidence to warrant rejection of the claim that the population mean is notequal to 87.7.O There is not sufficient evidence to warrant rejection of the claim that the population mean isnot equal to 87.7.O The sample data support the claim that the population mean is not equal to 87.7.O There is not sufficient sample evidence to support the claim that the population mean is notequal to 87.7.

Answered: You wish to test the following claim…

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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Related questions

Question

You wish to test the following claim (Ha) at a significance level of a = 0.005.
87.7
Ha:µ + 87.7
You believe the population is normally distributed, but you do not know the standard deviation.
data
98.2
101.2
89.2
90.1
96.6
100.7
a. What is the test statistic for this sample?
test statistic =
Round to 3 decimal places
b. What is the p-value for this sample?
p-value =
Round to 4 decimal places.
c. The p-value is...
O less than (or equal to) a
greater than a
d. This test statistic leads to a decision to...
O reject the null
O accept the null
O fail to reject the null
e. As such, the final conclusion is that...
O There is sufficient evidence to warrant rejection of the claim that the population mean is not
equal to 87.7.
O There is not sufficient evidence to warrant rejection of the claim that the population mean is
not equal to 87.7.
O The sample data support the claim that the population mean is not equal to 87.7.
O There is not sufficient sample evidence to support the claim that the population mean is not
equal to 87.7.

Expert Solution

Step 1

$G i v e n d a t a i s 98.2, 101.2, 89.2, 90.1, 96.6, 100.7 s a m p l e s i z e (n) = 6 s a m p l e m e a n (\bar{x}) = \frac{98.2 + 101.2 + 89.2 + 90.1 + 96.6 + 100.7}{6} s a m p l e m e a n (\bar{x}) = \frac{576}{6} s a m p l e m e a n (\bar{x}) = 96 s \tan d a r d d e v i a t i o n (S) = \sqrt{\frac{\sum_{i} {(X_{i} - \bar{x})}^{2}}{n - 1}} S = \sqrt{\frac{{(98.2 - 96)}^{2} + {(101.2 - 96)}^{2} + {(89.2 - 96)}^{2} + {(90.1 - 96)}^{2} + {(96.6 - 96)}^{2} + {(100.7 - 96)}^{2}}{6 - 1}} S = 5.2035$