Q1

No, it is not reasonable to calculate a confidence interval for the data.

Reason: the population standard deviation is not given.

Q2

We are given:

Margin of estimate, e = 0.10(100) hours

Level of confidence, C.I = 95%

Standard deviation, = 0.90 hours

Sample size, n =?

Sample size =

But at 95% level of confidence, z = 1.96 from tables

Hence,

n = = 311.1696

Therefore, the required sample size is 312.

Q3

We are given:

X=120

N=200

Sample proportion, p= = =0.6

Confidence interval of a population proportion = z

95% confidence interval = 0.61.96*

95% confidence interval =0.60.0679

95% confidence interval = (0.5321, 0.6679)

Yes. The proportion of the Georgetown country residents who believe that country’s real estate taxes are too high is between 0.5321 and 0.6679 at 95% level of confidence.

Q4

First, state the null and alternative hypothesis

: (No significant difference in the mean selection sales)

: (Atleast one of the means of the selection sales is different)

Where;

= the mean for soft drink selection sales

= the mean for new registers sales

=the mean for dairy selection sales

To test where a significant difference exists, a one-way ANOVA model is conducted using Ms-Excel.

Anova: Single Factor

SUMMARY

*Groups*

*Count*

*Sum*

*Average*

*Variance*

Column 1

5

40

8

11.5

Column 2

5

35

7

6.5

Column 3

5

43

8.6

4.3

ANOVA

*Source of Variation*

*SS*

*df*

*MS*

*F*

*P-value*

*F crit*

Between Groups

6.5333333

2

3.2666667

0.439462

0.65435

3.885294

Within Groups

89.2

12

7.4333333

Total

95.733333

14

Decision rule at 5% significance level: Reject the null hypothesis if F> F critical (Kreyszig, 2010).

F=0.439

F critical = 3.885

Since F observed is less than F critical, we fail to reject the null hypothesis since we do not have enough evidence. Therefore we conclude that there is no significant difference in the mean selection of Coca-Cola stacked at four locations of the store.

Reference

Kreyszig, E. (2010). *Advanced Engineering Mathematics, 10th Edition*. John Wiley & Sons.

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