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Jane Doe SYM 506 Inferential Statistics Hypothesis Testing and Research Summary Summary of Survey Results The topic of study chosen for this research summary was Makeup Consumers’ Purchasing Habits. A survey was developed to identify characteristics of makeup consumers and better understand their purchasing habits. This survey consisted of ten questions that were qualitative and quantitative in nature. Thirty women participated in the survey and provided their feedback. Of the ten questions answered, two were chosen for additional analysis:

• How many makeup products do you use on a daily basis?

• How much money do you typically spend on makeup semi-monthly?

Histograms were developed for each of these questions to help visually summarize the data collected.

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Number of Makeup Products

Number of Makeup Products Used Daily

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$10 up to $20

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Dollars Spent

Money Spent on Makeup Semi- Monthly

Some basic analysis was completed for each of the two variables, as summarized in the tables below. Variable One: Number of Makeup Products Used Daily

Mean 5.73 products

Median 5.00 products

Mode 5.00 products

Variance 13.10

Standard Deviation 3.62

Variable Two: Money Spent on Makeup Semi-Monthly

Mean $25.30

Median $20.00

Mode $20.00

Variance 200.77

Standard Deviation 14.17

Analysis continued with the second variable, as confidence intervals were developed at the .95, .90, and .98 levels. The end points of the 98% confidence interval are $31.78 and $18.82. This indicates that we can be 98% confident that the mean amount of money spent on makeup every two months is within that range. Data Analysis and Hypothesis Test Data analysis of the first and second variables continued through hypothesis testing. To determine the type of hypothesis test to conduct, I considered three things:

• Type of data (nominal or ratio/interval) - The questions for variable one and two solicited ratio/interval type data.

• Number of samples involved – There is one sample and two measures.

• Purpose – The purpose for this test would be to look for a relationship between the two variables.

With the type of data, number of samples, and purpose in mind, I chose to complete a regression hypothesis analysis. Excel Analysis Please see the following excerpt from the Excel document in which the data was analyzed.

Independent Variable - Money spent on makeup semi-monthly Dependent Variable - Number of makeup products used daily

Research Question - Does there seem to be a direct relationship between the two variables?

From the scatterplot, there seems to be a direct relationship with a positive correlation between the two variables of money spent semi-monthly and number of makeup products used daily.

y = 0.1765x + 1.2689 R² = 0.4773

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Money Spent on Makeup Semi-Monthly

Money Spent vs. Number of Makeup Products

Number of Products (Y)

Linear (Number of Products (Y))

Research Question - At the .05 significance level, can we conclude that the slope of the regression line is positive?

SUMMARY OUTPUT

Regression Statistics Multiple R 0.690838733 R Square 0.477258155 Adjusted R Square 0.458588803 Standard Error 2.663055457 Observations 30

ANOVA df SS MS F Significance F

Regression 1 181.2944644 181.2944644 25.56372415 2.37924E-05

Residual 28 198.5722023 7.091864367 Total 29 379.8666667

Coefficients Standard Error t Stat P-value

Intercept 1.268908621 1.007997225 1.258841383 0.21848231 Money Spent (X) 0.176459475 0.034900602 5.056058163 2.37924E-05

H0: β ≤ 0

H1: β > 0

df = 28

Reject H0 if t > 1.701 (Found in Appendix B.5)

5.056 > 1.701

We reject the null hypothesis because 5.056 is greater than 1.701. We can conclude that the regression line is positive at the .05 significance level.

R Square 0.458588803

Approximately 45% of variation in number of products used daily is explained by variation in money spent on makeup on a semi-monthly basis.

Raw Data Collected

Money Spent (X) Number of Products (Y)

10 5

1 0

7 3

50 10

20 4

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20 8

15 6

15 1

20 2

20 8

44 6

30 7

15 7

30 11

25 3

15 5

40 5

40 7

30 5

20 3

5 1

50 16

30 3

20 5

50 14

42 7

45 7

20 2