High Temperatures in January Daily weather observations for southwestern Pennsylvania for the first three weeks of January show daily high temperatures as follows in degrees Fahrenheit: 57 28 39 28 37 30 55 35 44 59 51 60 46 62 51 37 46 51 The normal standard deviation in high temperatures for this time period is usually no more than 8 degrees. A meteorologist believes that with the unusual trend in temperatures the standard deviation is greater. At =α0.01 , can we conclude that the standard deviation is greater than 8  degrees? Assume the variable is normally distributed. (a)State the hypotheses and identify the claim with the correct hypothesis.   :H0  ▼(Choose one) :H1  ▼(Choose one) This hypothesis test is a ▼(Choose one) test.         (b)Find the critical value(s). Round the answers to three decimal places, if necessary. If there is more than one critical value, separate them with commas. Critical value(s):   (c)Compute the test value. Round the sample standard deviation to three decimal places and the final answer to three decimal places.   =χ2

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 26PFA
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High Temperatures in January Daily weather observations for southwestern Pennsylvania for the first three weeks of January show daily high temperatures as follows in degrees Fahrenheit:


57
28
39
28
37
30
55
35
44
59
51
60
46
62
51
37
46
51
The normal standard deviation in high temperatures for this time period is usually no more than 8 degrees. A meteorologist believes that with the unusual trend in temperatures the standard deviation is greater. At =α0.01 , can we conclude that the standard deviation is greater than 8  degrees? Assume the variable is normally distributed.
(a)State the hypotheses and identify the claim with the correct hypothesis.

 

:H0  ▼(Choose one)

:H1  ▼(Choose one)

This hypothesis test is a ▼(Choose one) test.

 
 
 
 
(b)Find the critical value(s). Round the answers to three decimal places, if necessary. If there is more than one critical value, separate them with commas.
Critical value(s):
 
(c)Compute the test value. Round the sample standard deviation to three decimal places and the final answer to three decimal places.

 

=χ2
 

 

(d)Make the decision.

 

▼(Choose one) the null hypothesis.
 
 
 
(e)Summarize the results.

 

There ▼(Choose one) enough evidence to support the claim that the standard deviation is greater than 
8  degrees.
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