Question 6 A researcher would like to evaluate the effect of a new cold medicati

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Question 6

A researcher would like to evaluate the effect of a new cold medication on reaction time. It is known that under regular circumstances, the distribution of reaction time is normally distributed with a mean of 200 and a standard deviation of 8. The researcher believed that this new cold medication would decrease reaction time. If a sample of 25 participants revealed a mean of 198 for the new medication, use the .01 level of significance to answer the following questions below.

6. What statistical evidence can you provide for your decision?   

Question 7

A researcher would like to evaluate the effect of a new cold medication on reaction time. It is known that under regular circumstances, the distribution of reaction time is normally distributed with a mean of 200 and a standard deviation of 8. The researcher believed that this new cold medication would decrease reaction time. If a sample of 25 participants revealed a mean of 198 for the new medication, use the .01 level of significance to answer the following questions below.

7. What final conclusion can be made within the context of this example?

There is sufficient evidence to indicate the new cold medication would decrease reaction time.

There is insufficient evidence to indicate the new cold medication would keep reaction time the same.

There is insufficient evidence to indicate the new cold medication would decrease reaction time.

There is insufficient evidence to indicate the new cold medication would change the reaction time.

Question 8

A researcher would like to evaluate the effect of a new cold medication on reaction time. It is known that under regular circumstances, the distribution of reaction time is normally distributed with a mean of 200 and a standard deviation of 8. The researcher believed that this new cold medication would decrease reaction time. If a sample of 25 participants revealed a mean of 198 for the new medication, use the .01 level of significance to answer the following questions below.

8. What are the assumptions associated with making inferences back to the population?

scores are normally distributed in the sample, subjects (or scores) are dependent

scores are normally distributed in the population, subjects (or scores) are dependent

scores are normally distributed in the sample, subjects (or scores) are independent of each other

scores are normally distributed in the population, subjects (or scores) are independent of each other

Question 9

A researcher would like to evaluate the effect of a new cold medication on reaction time. It is known that under regular circumstances, the distribution of reaction time is normally distributed with a mean of 200 and a standard deviation of 8. The researcher believed that this new cold medication would decrease reaction time. If a sample of 25 participants revealed a mean of 198 for the new medication, use the .01 level of significance to answer the following questions below. If the researcher in this scenario decided to conduct a 2-tail test at the .01 level of significance, answer the following questions:

1. What are the null and alternative hypotheses?

H0: > 198; H1: < 198

H0: = 198; H1: 198

H0: = 200; H1: 200

H0: > 200; H1: < 200

Question 10

A researcher would like to evaluate the effect of a new cold medication on reaction time. It is known that under regular circumstances, the distribution of reaction time is normally distributed with a mean of 200 and a standard deviation of 8. The researcher believed that this new cold medication would decrease reaction time. If a sample of 25 participants revealed a mean of 198 for the new medication, use the .01 level of significance to answer the following questions below. If the researcher in this scenario decided to conduct a 2-tail test at the .01 level of significance, answer the following questions:

2. What is the confidence interval?   

There is sufficient evidence to indicate the new cold medication would decrease reaction time.

There is insufficient evidence to indicate the new cold medication would keep reaction time the same.

There is insufficient evidence to indicate the new cold medication would decrease reaction time.

There is insufficient evidence to indicate the new cold medication would change the reaction time.

Explanation / Answer

Given that,
population mean(u)=200
standard deviation, =8
sample mean, x =198
number (n)=25
null, Ho: >200
alternate, H1: <200
level of significance, = 0.01
from standard normal table,left tailed z /2 =2.326
since our test is left-tailed
reject Ho, if zo < -2.326
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 198-200/(8/sqrt(25)
zo = -1.25
| zo | = 1.25
critical value
the value of |z | at los 1% is 2.326
we got |zo| =1.25 & | z | = 2.326
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value : left tail - ha : ( p < -1.25 ) = 0.10565
hence value of p0.01 < 0.10565, here we do not reject Ho

ANSWERS
---------------
6. we do not have enough evidence to support the claim
7(c).There is insufficient evidence to indicate the new cold medication would decrease reaction time.
8(d).scores are normally distributed in the population, subjects (or scores) are independent of each other
9(d).null, Ho: >200
alternate, H1: <200
test statistic: -1.25
critical value: -2.326
decision: do not reject Ho
p-value: 0.10565

10.confidence interval is 99%

Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=200
Standard deviation( sd )=8
Sample Size(n)=25
Confidence Interval = [ 200 ± Z a/2 ( 8/ Sqrt ( 25) ) ]
= [ 200 - 2.58 * (1.6) , 200 + 2.58 * (1.6) ]
= [ 195.87,204.13 ]

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