berunder theighting con.different conditions The expetive illusions was 6.72 under the bright coMyStatLabconditions, a difference that was not significant, r(19)-1.62." Expresult to a person who has never had a course in statistics. Be surresearchers reThe'collegeat the beginning and end of their first year ofthe results in the following table12 A study was done of personality characteristics of 100 students who weresketches of the distributions in your answerDifferenceSpringSDMFall3.84SD1.50*15.32Personality ScaleAnxietyDepression4.218.913.08186.2416.828.397.11-2360.1289 326.876.022289*37.2259 895.394.2Introversion38.11NeuroticismDA 05,p

Question
Asked Oct 16, 2019

In each of the following studies, a single samples mean is being compared to a population with a known mean but an unknown variance. For each study, decide whether thee result is significnt.  (only a and b) 

ber
under the
ighting con.
different conditions The expe
tive illusions was 6.72 under the bright co
MyStatLab
conditions, a difference that was not significant, r(19)-1.62." Exp
result to a person who has never had a course in statistics. Be sur
researchers re
The
'college
at the beginning and end of their first year of
the results in the following table
12 A study was done of personality characteristics of 100 students who were
sketches of the distributions in your answer
Difference
Spring
SD
M
Fall
3.84
SD
1.50*
15.32
Personality Scale
Anxiety
Depression
4.21
8.91
3.08
1
86.24
16.82
8.39
7.11
-23
60.12
89 32
6.87
6.02
22
89*
37.22
59 89
5.39
4.2
Introversion
38.11
Neuroticism
DA 05,p<.01
(a) Focusing on the difference scores, figure the t values for each personal
scale. (Assume that SD in the table is for what we have called S, the unbiase
(b) Explain to a person who has never had a course in statistics what this tabl
estimate of the population standard deviation.)
means
Set II
13. In each of the following studies, a single sample's mean is being compared to
a population with a known mean but an unknown variance. For each study, de-
tatLab
cide whether the result is significant.
Estimated
Population
Standard
Sample
Size (N)
Population
Mean (u)
Sample
Mean (M)
Deviation
Significance
Level (a)
(S)
Tails
(a)
16
100.31
2.00
100.98
1 (high predicted)
(b)
16
05
.47
4.00
.00
2
16
68.90
.05
9.00
34.00
1 (low predicted)
.01
14. Evolutionary theories often emphasize that humans have adapted to their physi
cal environment. One such theory hypothesizes that people should spontane-
ously follow a 24-hour cycle of sleeping and waking-even if they are not
99
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ber under the ighting con. different conditions The expe tive illusions was 6.72 under the bright co MyStatLab conditions, a difference that was not significant, r(19)-1.62." Exp result to a person who has never had a course in statistics. Be sur researchers re The 'college at the beginning and end of their first year of the results in the following table 12 A study was done of personality characteristics of 100 students who were sketches of the distributions in your answer Difference Spring SD M Fall 3.84 SD 1.50* 15.32 Personality Scale Anxiety Depression 4.21 8.91 3.08 1 86.24 16.82 8.39 7.11 -23 60.12 89 32 6.87 6.02 22 89* 37.22 59 89 5.39 4.2 Introversion 38.11 Neuroticism DA 05,p<.01 (a) Focusing on the difference scores, figure the t values for each personal scale. (Assume that SD in the table is for what we have called S, the unbiase (b) Explain to a person who has never had a course in statistics what this tabl estimate of the population standard deviation.) means Set II 13. In each of the following studies, a single sample's mean is being compared to a population with a known mean but an unknown variance. For each study, de- tatLab cide whether the result is significant. Estimated Population Standard Sample Size (N) Population Mean (u) Sample Mean (M) Deviation Significance Level (a) (S) Tails (a) 16 100.31 2.00 100.98 1 (high predicted) (b) 16 05 .47 4.00 .00 2 16 68.90 .05 9.00 34.00 1 (low predicted) .01 14. Evolutionary theories often emphasize that humans have adapted to their physi cal environment. One such theory hypothesizes that people should spontane- ously follow a 24-hour cycle of sleeping and waking-even if they are not 99

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Step 1

a)

It is given that sample size is 16, sample mean (M) is 100.98, population mean is 100.31 and test is right tailed. The level of significance is 0.05.

Step 2

The hypotheses to be tested are:

H0: μ =100.31, that is, true mean is equal to 100.31.

Ha: μ >100.31, that is, true mean is greater than 100.31.

Here, the population standard deviation, σ, is unknown; it is estimated by the sample standard deviation as, s = 2.00. So, in order to test whether the mean is greater than 100.31, the t test must be used.

The test statistic is found as follows:

М-и
100.98-100.31
2.00
V16
1.34
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М-и 100.98-100.31 2.00 V16 1.34

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Step 3

p-value:

For sample size n, the degrees of freedom (df) is n – 1. Here, df = 16 – 1 = 15.

The p-value using Excel formula “=1–T.DIST(1.34,15,TRUE)”­ is approximately 0.1001.

Rejection rule:

Reject the null hypothesis if p-value is less than the level of significance.

Conclusion:

The p-value is 0.1001 and the level of significance i...

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