Question

A teacher claims 9 year old girls are taller than 9 year old boys. Test this claim at an alpha level of .05. A researcher randomly selected a smaple of 60 boys and sample of 50 girls.

Boys: n=60 mean = 123.5 cm standard deviation = 9.9 cm

Girls: n=50 mean = 126.2 cm standard deviation = 10.9 cm

Use either one sample t or z test. Label critical value and test value. State p value and show all five steps of analysis.

Answer #1

Answer)

Null hypothesis Ho : u 1 = u 2

Alternate hypothesis Ha : u 1 < u 2

Where u 1 is for boys and u 2 is for girls

As the population s.d is unknown and we are given with sample s.d, we will use t test

Test statistics z = (u1-u2)/standard error

Standard error = √{(s1^2/n1)+(s2^2/n2)}

u1 = 123.5, u2 = 126.2

N1 = 60, N2 = 50

S1 = 9.8, S2 = 10.9

Test statistics t = -1.348

Degrees of freedom is = smaller of n1-1, n2-1

Df = 49

For df 49 and alpha 0.05, critical value from t distribution is = -1.677

And P-Value for -1.348 test statistics is = 0.0919

As the obtained P-Value is greater than 0.05(given significance level)

We fail to reject the null hypothesis

And we do not have enough evidence to support the claim

The population mean of the heights of five-year old boys is 100
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2.
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a researcher claims that the mean head circumference of a two
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using this sample and that the standard deviation of the sample is
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Ho: CV: Test Statistic
H1:

A doctor claims that teenage boys get more screen time as
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boys' screen time
girls' screen time
5
3
4
4
6
5
5
4
4
3
5
4
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3
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Sample Mean:...

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The heights of 11-year old boys in the United States are
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