
a.
Find a 95% confidence interval for the difference between the bullish sentiment measures for the most recent two weeks.
a.

Answer to Problem 47SE
The 95% confidence interval for the difference between the bullish sentiment measures for the most recent two weeks is
Explanation of Solution
Calculation:
It is given that the bullish sentiment of individual investors for the week end was 27.6%, 48.7% for one week earlier and 39.7% for one month earlier. A sample of 240 is considered.
Confidence interval:
The
where
Here,
Software procedure:
Step-by-step software procedure to obtain the p-value using MINITAB software is as follows,
- Choose Stat > Basic Statistics > 2 Proportions.
- Choose Summarized data.
- In First sample, enter Trials (n) as 240 and Events as (x) 66.
- In Second sample, enter Trials (n) as 240 and Events as 117.
- Click Options.
- In Confidence level, Enter 95.
- In Alternative select not equal.
- Click OK in all dialogue boxes.
Output using MINITAB software is as follows,
Thus, the 95% confidence interval is
Interpretation:
There is 95% confidence that the difference between the bullish sentiment measures for the most recent two weeks lies between –0.297 and –0.127.
b.
State the null and alternative hypothesis so that rejection of the null hypothesis will allow to conclude that the most recent bullish sentiment is weaker than that of one month ago.
b.

Answer to Problem 47SE
The null and alternative hypotheses are given below:
Null hypothesis:
Alternative hypothesis:
Explanation of Solution
Calculation:
Here
State the hypothesis:
The test hypotheses are as follows,
Null hypothesis:
That is, the proportion of the bullish sentiment of individual investors for the most recent week is greater than the proportion of the bullish sentiment of individual investors for one month ago.
Alternative hypothesis:
That is, the proportion of the bullish sentiment of individual investors for the most recent week is less than the proportion of the bullish sentiment of individual investors for one month ago.
c.
Test the hypothesis in part (b) at
c.

Answer to Problem 47SE
There is sufficient evidence to conclude that, there is decrease in bullish sentiment over the past month.
Explanation of Solution
Calculation:
Test statistic:
The test statistic for hypothesis tests about
Where
Software procedure:
Step-by-step software procedure to obtain the p-value using MINITAB software is as follows,
- Choose Stat > Basic Statistics > 2 Proportions.
- Choose Summarized data.
- In First sample, enter Trials (n) as 240 and
Events as (x) 66. - In Second sample, enter Trials (n) as 240 and Events as 95.
- Click Options.
- In Confidence level, Enter 99.
- In Alternative select less than.
- Click OK in all dialogue boxes.
Output using MINITAB software is as follows,
Thus, the p-value is 0.002.
Rejection rule:
If the
If the
Conclusion:
Here the p-value 0.002 is less than the significance level 0.01.
That is,
Thus, the null hypothesis is rejected.
Therefore, there is sufficient evidence to conclude that, the proportion of the bullish sentiment of individual investors for the most recent week is less than the proportion of the bullish sentiment of individual investors for one month ago.
Interpretation:
Here the null hypothesis
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Chapter 10 Solutions
EBK STATISTICS FOR BUSINESS & ECONOMICS
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