Statistics

By Dr Tony Halim

GBA: 27 February 2013

Done by:

Koh En Song Andrew (Q1211397)

Melissa Teo Kah Leng (E1011088)

Woon Wei Jie Jared

T 04

1.

Over the span of 100 days, the total revenue for Unicafe North and Unicafe West is $21876.60 and $22042.00 respectively. The average revenue for Unicafe North is $218.77. The average revenue for Unicafe West is $220.42. The highest revenue occurred on the 88th day for both outlets. The lowest revenue occurred on 39th day for both outlets. Generally, both outlets earn roughly the same amount of revenue each day.

2a.

Confidence interval is a range of values constructed from sample data so that the population parameter is likely to occur within that range at a specific probability (Lind, Marchal & Wathen, 2013).

Using the 95% level of confidence, the confidence interval for Unicafe West is 220.42 6.211. The confidence interval limits are $214.21 and $226.63 (rounded off to 2 decimal places). Using the 95% level of confidence, the confidence interval for Unicafe North is 218.766 5.571. The confidence interval limits are $213.20 and $224.34 (rounded off to 2 decimal places). In the event that Mr Yeung wants to predict his potential revenue for the next one hundred days, 95% of the confidence intervals would be expected to contain the population mean. The remaining 5% of the confidence intervals would not contain the population mean, average revenue earned per day.

Mr Yeung has correctly estimated that the revenue from both outlets is the same.

2b.

Subsequent samples of 100 days may not contain the population mean of this confidence interval as a result of sampling error. Since this confidence interval was obtained from a specific duration of 100 days, it is unlikely that subsequent sample of 100 days would have the exact population mean every time. Sampling errors are random and quite unlikely to occur so it is a reasonable assumption.

The sampled population is also assumed to be normal or approximately normal.2c.

The level of confidence and the size of the standard error of the mean would affect the width of the confidence interval.

A large sample would decrease the size of the standard error, decreasing the width of the confidence interval. A small sample would increase the size of the standard error, widening the width of the confidence interval. Larger sample sizes are normally more costly and time-consuming.

As the level of confidence decreases, the width of the confidence interval decreases. As the level of confidence increases, the width of the confidence interval increases. A larger level of confidence would imply a greater certainty of obtaining the population mean.

3a.

According to Lind et al. (2013), hypothesis is a statement about a population, subjected to verification Hypothesis testing is a statistical procedure used to determine whether the hypothesis is true and should not be rejected, or if it is not true and should be rejected (Lind et al., 2013).

The null and alternate hypothesis is as such

H0: µN - µW ≤ 0

H1: µN - µW > 0

Where µN is the mean wastage for UniCafe North

µw is the mean wastage for UniCafe West

As the mean wastage of UniCafe North is significantly higher than UniCafe West, the alternate hypothesis (i.e., claim) is denoted as H1: µN - µW > 0. Since the null hypothesis is opposite of the claim, it is denoted as H0: µN - µW ≤ 0.

3b.

The pooled t test analysis of wastage by outlet, where α = 0.05, is as such

t Test

UniCafe West-UniCafe North

Assuming equal variances

| | | |

Difference| -22.758| t Ratio| -24.6523|

Std Err Dif| 0.923| DF| 198|

Upper CL Dif| -20.938| Prob > |t|| <.0001*|

Lower CL Dif| -24.578| Prob > t| 1.0000|

Confidence| 0.95| Prob < t| <.0001*|

The test statistic is -24.6523. It noted that the test statistics is based on UniCafe...