EBK STATISTICS FOR BUSINESS & ECONOMICS
EBK STATISTICS FOR BUSINESS & ECONOMICS
12th Edition
ISBN: 8220100460463
Author: Anderson
Publisher: CENGAGE L
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Chapter 10, Problem 47SE

a.

To determine

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

a.

Expert Solution
Check Mark

Answer to Problem 47SE

The 95% confidence interval for the difference between the bullish sentiment measures for the most recent two weeks is (0.297,0.127).

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 interval estimate of the difference between two population proportions is,

Confidence interval=p¯1p¯2±zα2p¯1(1p¯1)n1+p¯2(1p¯2)n2

where 1α is the confidence coefficient, p¯1and p¯2 the point estimates for population proportion, n1and n2 are sample sizes for the two group..

Here, n1=n2=n3=240,p¯1=0.276,p¯2=0.487,p¯3=0.397,  and

x1=(240)(0.276)=66.2466

x2=(240)(0.487)=116.88117

x3=(240)(0.397)=95.2895

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,

EBK STATISTICS FOR BUSINESS & ECONOMICS, Chapter 10, Problem 47SE , additional homework tip  1

Thus, the 95% confidence interval is (0.297,0.127).

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.

To determine

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.

Expert Solution
Check Mark

Answer to Problem 47SE

The null and alternative hypotheses are given below:

Null hypothesis: H0:p1p30

Alternative hypothesis: Ha:p1p3<0

Explanation of Solution

Calculation:

Here p1 represents the proportion of the bullish sentiment of individual investors for the most recent week and p3 represents the proportion of the bullish sentiment of individual investors for one month ago.

State the hypothesis:

The test hypotheses are as follows,

Null hypothesis:

H0:p1p30

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:

Ha:p1p3<0

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.

To determine

Test the hypothesis in part (b) at α=0.01 and make a conclusion.

c.

Expert Solution
Check Mark

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 p1p3 is,

z=(p¯1p¯3)p¯(1p¯)(1n1+1n2)

Where p¯1and p¯2 the point estimates for population proportion, n1and n2 are sample sizes for the two groups, and p¯ is the pooled proportion

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,

EBK STATISTICS FOR BUSINESS & ECONOMICS, Chapter 10, Problem 47SE , additional homework tip  2

Thus, the p-value is 0.002.

Rejection rule:

If the pvalueα, then reject the null hypothesis.

If the pvalue>α, then do not eject the null hypothesis.

Conclusion:

Here the p-value 0.002 is less than the significance level 0.01.

That is, p-value(0.002)<α(0.01)

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 H0 is rejected. That is, there is decrease in bullish sentiment over the past month.

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Chapter 10 Solutions

EBK STATISTICS FOR BUSINESS & ECONOMICS

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