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Making Inferences About the Population and Testing Hypotheses

Making Inferences About the Population and Testing Hypotheses. Null Hypothesis. Statement about a status quo Conservative statement No difference Any change likely due to random error Purpose: provide an opportunity to nullify it -- or prove it false We want to reject the null.

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Making Inferences About the Population and Testing Hypotheses

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  1. Making Inferences About the Population and Testing Hypotheses

  2. Null Hypothesis • Statement about a status quo • Conservative statement • No difference • Any change likely due to random error • Purpose: provide an opportunity to nullify it -- or prove it false • We want to reject the null

  3. Alternative Hypothesis • Opposite of null • There is a difference • State direction of difference • Ho: There is no difference in likelihood to return to a restaurant between customers who are highly satisfied and those who are less satisfied • H1: Customers who are more satisfied will be more likely to return to a restaurant in the future than those who are not

  4. Steps in Hypothesis Testing • Begin with a statement about what you believe exists in the population (population mean) • Draw a random sample and calculate the sample mean • Compare the sample mean to the hypothesized population parameter • Decide whether the sample supports the original hypothesis and state conclusions. Reject null or fail to reject null.

  5. Example • Null Hypothesis: Customers are neither satisfied nor dissatisfied with their past dining experience at Central Station Restaurant (µ = 50) • Alternative Hypothesis: Customers are either satisfied or dissatisfied

  6. Testing a Hypothesis About a Mean • Use SPSS • Select STATISTICS -- COMPARE MEANS -- ONE SAMPLE t TEST • Select the variable(s) of interest (e.g. performance, satisfaction, loyalty, demographics -- interval or ratio level) • Enter amount hypothesized as the test value

  7. T-Test One Sample Statistics Satisfaction (0%-100%) N = 89 Mean=61.49 s = 41.99 One-Sample Test (Test Value = 50) t-value = 2.582 (88 df) Significance (p-value) = .011 Mean difference = 11.49 95% Confidence Interval of the difference 2.6483 to 20.3404 LL = 50 + 2.6483 = 52.65 UL = 50 + 20.3404 = 70.34 We reject the null hypothesis that people are neither satisfied nor dissatisfied and conclude they are satisfied with their experience at Central Station with a range of between 52.65 to 70.34. We are 95% confident that the population satisfaction level is contained within this range.

  8. Testing for Significant Differences between Two Groups • Sometimes we are interested in testing whether or not there are statistically significant differences between subgroups of respondents

  9. Testing a Hypothesis About a Mean • Use SPSS • Select STATISTICS -- COMPARE MEANS -- INDEPENDENT SAMPLES t TEST • Select the variable(s) of interest (e.g. performance, satisfaction, loyalty) and a Grouping Variable (only 2 levels) • Specify the values of the grouping variable (response values)

  10. Example • Null Hypothesis: There is no difference between men & women and their level of satisfaction • Alternative Hypothesis: Men will be less satisfied than women with their dining experience at Central Station

  11. Results Gender Sample Mean Std. Deviation Male 45 53.71 6.53 Female 44 69.45 5.87 F-test = 4.31 (p=.041) for equal variances. T-test value for equality of means = -1.790 (df=87) p-value=.077 Conclude there is a statistically significant difference between men & women. Women are more satisfied than men.

  12. Testing for Differences Between 2 or more Groups • Use Analysis of Variance • STATISTICS -- COMPARE MEANS - ONE-WAY ANOVA • Specify the independent variable (grouping variable) • Specify dependent variable (interval or ratio level variable) • Options - Descriptive • Post Hoc -- Scheffe

  13. Example • Null Hypothesis: There is no difference between income groups and their level of satisfaction (µ1 = µ2 = µ3 = µ4) • Alternative Hypothesis: Individuals with higher incomes are more likely to be satisfied than than individuals with lower incomes (µ1 = µ2) < (µ3 = µ4)

  14. Results Group N Mean  $19,999 39 49.51 $20,000 - $34,999 16 57.75 $35,000 - $54,999 11 73.89 $55,000 - $74,999 9 81.89 $75,000 and over 14 76.36 Overall 89 61.49 ANOVA - F = 2.136 p = .083(There are significant differences) POST HOC TESTS None were significant Conclusions: Those with incomes above $35,000 reported higher levels of satisfaction than those with incomes less than $34,999. Alternative hypothesis partially supported.

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