Some individuals have the ability to recall accurately vast amounts of autobiogr
ID: 3240481 • Letter: S
Question
Some individuals have the ability to recall accurately vast amounts of autobiographical information without mnemonic tricks or extra practice. This ability is called HSAM, for Highly Superior Autobiographical Memory. A study recruited adults with confirmed HSAM and control individuals of similar age without HSAM. All study participants were given a battery of cognitive and behavioral tests in the hope of finding out how this extraordinary ability works. Here are the participants' results for a visual memory test
(a) Calculate:
x¯¯¯H
(±
0.001) =
x¯¯¯C
(±
0.001) =
sH
(±
0.001) =
sC
(±
0.001) =
SE
(±
0.001) =
t
(±
0.001) =
df (±
0.1) =
P
(±
0.001 (Use software)) =
(b) Is there significant evidence that individuals with HSAM have higher visual memory test scores than typical individuals, on average:
A study of the effects of exercise used rats bred to have high or low capacity for exercise. The 8 high-capacity rats had mean blood pressure 89 and standard deviation 9; the 8 low-capacity rats had mean blood pressure 105 with standard deviation 13. (Blood pressure is measured in millimeters of mercury.)True or False.
The two-sample t statistic for comparing the two population means has value 0.5
Explanation / Answer
Solution:-
1) False.
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 - 2 = 0
Alternative hypothesis: 1 - 2 0
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
S.E = sqrt[(s12/n1) + (s22/n2)]
S.E = 5.59
DF = 14
t = [ (x1 - x2) - d ] / SE
t = - 2.862
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 40 degrees of freedom is more extreme than -1.99; that is, less than -1.99 or greater than 1.99.
Thus, the P-value = 0.01255
Interpret results. Since the P-value (0.01255) is less than the significance level (0.05), we cannot accept the null hypothesis.
2)
Yes.
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1< 2
Alternative hypothesis: 1 > 2
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 0.5505
DF = 90
t = [ (x1 - x2) - d ] / SE
t = 5.09
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of 5.09. We use the t Distribution Calculator to find P(t > 5.09) = less than 0.00001
Therefore, the P-value in this analysis is less than 0.00001
Interpret results. Since the P-value (0.00001) is less than the significance level (0.01), we have to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that young adult males with tongue piercing have significantly more enamel cracks.
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