Question

2:57:43 remainin The average final exam score for the statistics course is 82%. A professor wants to see if the average final exam score for students who are given colored pens on the first day of class is lower. The final exam scores for the 12 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 82, 58, 82, 87, 74, 80, 71, 85, 79, 60, 65, 64 What can be concluded at the the a -0.10 level of significance level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: HO: ? 7c H: ? 7 c. The test statistic ? - (please show your answer to 3 decimal places.) d. The p-value (Please show your answer to 4 decimal places.) e. The p-value is a f. Based on this, we should Select an answer the null hypothesis. 8. Thus, the final conclusion is that ... The data suggest the population mean is not significantly lower than 82 at a = 0.10, so there is statistically insignificant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is equal to 82. The data suggest the populaton mean is significantly lower than 82 at a -0.10, so there is statistically significant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is lower than 82. The data suggest that the population mean final exam score for students who are given colored pens at the beginning of class is not significantly lower than 82 ata -0.10, so there is statistically insignificant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is lower than 82.

Answer 1

Given that,
population mean(u)=82
sample mean, x =73.9167
standard deviation, s =10.0946
number (n)=12
null, Ho: μ=82
alternate, H1: μ<82
level of significance, α = 0.1
from standard normal table,left tailed t α/2 =1.363
since our test is left-tailed
reject Ho, if to < -1.363
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =73.9167-82/(10.0946/sqrt(12))
to =-2.774
| to | =2.774
critical value
the value of |t α| with n-1 = 11 d.f is 1.363
we got |to| =2.774 & | t α | =1.363
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :left tail - Ha : ( p < -2.7739 ) = 0.00905
hence value of p0.1 > 0.00905,here we reject Ho
ANSWERS
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a.
T test for single mean with unknown population standard deviation
b.
null, Ho: μ=82
alternate, H1: μ<82
c.
test statistic: -2.774
critical value: -1.363
d.
p-value: 0.00905
e.
p value is less than alpha value
f.
decision: reject Ho
g.
we have enough evidence to support the claim that population mean score for students who are given colored pens at the begining of class is lower than 82