# Food for Fork - Statistics Case Study

Pages: 17 (4086 words) Published: April 8, 2013
Food for Fork

Case Study
by
Tony Mayer

1. Is the average amount that people are willing to pay for an entrée less than the forecast value of \$19? 2.1. Null and alternate hypotheses
H0: Average amount people are willing to pay for entrée = \$19 HA: Average amount people are willing to pay for entrée < \$19

2.2. Statistical technique chosen to test the hypothesis One sample t-test

2.3. Summary of the nature (characteristics) of the test selected

2.4. SPSS Test
One-Sample Statistics|
| N| Mean| Std. Deviation| Std. Error Mean|
What would you expect an average evening meal to be priced?| 400| \$19.2300| \$7.55943| \$0.37797|

One-Sample Test|
| Test Value = 19|
| t| df| Sig. (2-tailed)| Mean Difference| 95% Confidence Interval of the Difference| | | | | | Lower| Upper|
What would you expect an average evening meal to be priced?| .609| 399| .543| \$0.23000| -\$0.5131| \$0.9731|

2.5. Test results
Mean: 19.23
Mean difference: 0.23
Std. deviation: 7.56
Test statistic: .609
P-value: .543

Data values are independent. Random sample from less than 10% of the population (400/500,000*100=0.08%). It is assumed that the population follows a normal model.

2.6. Graphical representation of the results

2.7. Description for the graphical output

2.8. Statistical interpretation
A one-sample t-test was used to determine whether the average amount people are willing to pay for entrée is less than \$19. The mean difference (0.23) was not statistically significant (p-value=0.543). Therefore we cannot reject the null hypothesis.

2.9. Non-statistical interpretation

2. Does the average income of the people surveyed differ from \$70,000? 3.10. Null and alternate hypotheses
H0: Average income of people surveyed = \$70,000
HA: Average income of people surveyed ≠ \$70,000

3.11. Statistical technique chosen to test the hypothesis One sample t-test

3.12. Summary of the nature (characteristics) of the test selected

3.13. SPSS Test
One-Sample Statistics|
| N| Mean| Std. Deviation| Std. Error Mean|
What is your annual salary?| 400| 77087.5000| 28896.92760| 1444.84638|

One-Sample Test|
| Test Value = 70000|
| t| df| Sig. (2-tailed)| Mean Difference| 95% Confidence Interval of the Difference| | | | | | Lower| Upper|
What is your annual salary?| 4.905| 399| .000| 7087.50000| 4247.0371| 9927.9629|

3.14. Test results
Mean: 77,087.50
Mean difference: 7,087.50
Std. deviation: 28,896.93
Test statistic: 4.91
P-value: .000

Data values are independent. Random sample from less than 10% of the population (400/500,000*100=0.08%). It is assumed that the population follows a normal model.

3.15. Graphical representation of the results

3.16. Description for the graphical output

3.17. Statistical interpretation
A one-sample t-test was used to determine whether the average income of people surveyed differed from \$70,000. The mean difference (7,087.50) was statistically significant (p-value=0.000). Therefore we can reject the null hypothesis and accept the alternative.

3.18. Non-statistical interpretation

3. Is there a difference in preference for simple décor and elegant décor? If so, which is preferred? 4.19. Null and alternate hypotheses
H0: Preference for simple décor = Preference for elegant décor HA: Preference for simple décor ≠ Preference for elegant décor

4.20. Statistical technique chosen to test the hypothesis Paired samples test (to test hypothesis)
Chi-squared test (for representation)

4.21. Summary of the nature (characteristics) of the test selected

4.22. SPSS Test
Paired Samples Statistics|
| Mean| N| Std. Deviation| Std. Error Mean|
Pair 1| Prefer Simple Decor| 2.26| 400| 1.212| .061|
| Prefer Elegant Decor| 3.64| 400|...