# Food for Fork - Statistics Case Study

**Topics:**Statistics, Student's t-test, Statistical hypothesis testing

**Pages:**17 (4086 words)

**Published:**April 8, 2013

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|...

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