Question

A researcher knows that the mean of all IQ scores is 100.

She gives 30 days of hot breakfast to 16 fifth graders and then tests their IQ. She finds

110,114,101,99,98,93,104,103,100,100,107,120,115,105,98,97.

Conduct a one sample t-test and report the finding.  Does hot breakfast increase IQ?

Answer 1

Answer:-

Given That:-

A researcher knows that the mean of all IQ scores is 100. She gives 30 days of hot breakfast to 16 fifth graders and then tests their IQ. She finds 110,114,101,99,98,93,104,103,100,100,107,120,115,105,98,97.

Conduct a one sample t-test and report the finding.  Does hot breakfast increase IQ?

Given,

X	X - ma=ean	(X - mean)2
110	6	36
114	10	100
101	-3	9
99	-5	25
98	-6	36
93	-11	121
104	0	0
103	-1	1
100	-4	16
100	-4	16
107	3	9
120	16	256
115	11	121
102	1	1
98	-6	36
97	-7	49

Where n is the number of data points

Now

and

n = 16

This imples that

n = 16

variance (s2) = 832/15

= 55.4667

Standard Deviation (s) =

Standard Deviation(s) = 7.4476

n = 16

s = 7.45

The Test hypothesis is

Null Hypothesis is

Alternative Hypothesis  

This is one-sided test because the alternative hypothesis is formulated to detect the difference from the hypothesized mean on the upper side

Now, the value of test static can be found out by following formula:

Since the sample size is n = 16

degrees of freedom on the t - test statistic are n - 1 = 16 - 1

= 15

This implies that

Since

we reject the null hypothesis

alternative hypothesis at  

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