T-Test Hypothesis

T-Test Hypothesis

SPSS assignment 

[1]  Refer to the Softdrinks Corrected Database file and questionnaire for answering the following questions. 

  1. a)     In today’s world of obesity, which demographic and psychographicvariables are the best forecasters of the percentage of sugared soft drinks a person drinks?
  2. b)     Do Caucasian Americans drink significantly more soda on average than African Americans? c)     Investigate how many people in the sample are brand loyal? Assume that people are brand loyal if they drink a simple majority (more than 50%) of their favorite drinks.

[2]  Please refer to the Discover database and questionnaire for answering the following questions.

  1. a)    Please test that the mean overall satisfaction and the mean “value of the Discover card” to customers are significantly above 3.5.
  2. b)    Is the likelihood of a person keeping the card related significantly more to the value they have for the card or to their satisfaction with the card? Is the likelihood of a person recommending the card related more to its value or to the satisfaction perceived by the customer?
  3. c)    Is there a significant difference between how consumer’s rate courtesy and friendliness of a customer service agent?  Is there a significant difference between how consumers perceive professionalism and efficiency of handling the customer service call?  Finally, is there a significant difference between the customer’s ratings of the rep’s concern for her needs and the reps’ ability to make the customer feel important?  Does it make sense to measure these three questions using two survey items each? 

Solution

[1]

(a)

The demographic and psychographic factors that may be the forecasters of the percentage of sugared soft drinks a person drinks are – ethnic orientation, gender, classification and age.

Between-Subjects Factors
Value Label N
ethnic orientation 1 caucasian 362
2 African-American 59
gender 0 male 188
1 female 233
classification 1 freshman 38
2 sophomore 49
3 junior 75
4 senior 214
5 grad student 45
age 1 0-18 years 19
2 19-20 years 92
3 21-22 years 162
4 23-25 years 77
5 26-30 17
6 over 30 54

We apply a multiple regression to investigate the statistically significant predictors (among these 4 demographic and psychographic factors) of the percentage of sugared soft drinks a person drinks.

Variables Entered/Removeda
Model Variables Entered Variables Removed Method
1 age, ethnic orientation, gender, classificationb . Enter
a. Dependent Variable: % soft drinks with sugar
b. All requested variables entered.
Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .246a .061 .052 36.256
a. Predictors: (Constant), age, ethnic orientation, gender, classification
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression 35325.570 4 8831.392 6.719 .000b
Residual 546826.744 416 1314.487
Total 582152.314 420
a. Dependent Variable: % soft drinks with sugar
b. Predictors: (Constant), age, ethnic orientation, gender, classification
Coefficientsa
Model Unstandardized Coefficients Standardized Coefficients t Sig. 95.0% Confidence Interval for B
B Std. Error Beta Lower Bound Upper Bound
1 (Constant) 88.242 8.730 10.108 .000 71.082 105.401
ethnic orientation 9.406 5.101 .088 1.844 .066 -.620 19.432
gender -14.822 3.612 -.198 -4.104 .000 -21.921 -7.722
classification -1.194 1.759 -.036 -.678 .498 -4.652 2.265
age -4.082 1.472 -.147 -2.773 .006 -6.976 -1.189
a. Dependent Variable: % soft drinks with sugar

The factors ethnic orientation and classification are not statistically significant in predicting the percentage of sugared soft drinks a person drinks as their p-value is higher than 0.05

The p-value for the factors gender and age are very low and hence they are statistically significant in predicting the percentage of sugared soft drinks a person drinks.

Hence, the demographic and psychographic factors which are the best predictors of the percentage of sugared soft drinks a person drinks are – gender and age.

(b)

Our aim is to investigate whether Caucasian Americans drink significantly more soda on average than African Americans. We formulate the following hypothesis:

H0: On average, the Caucasian Americans and the African Americans drink same amount of soda.

H1: The Caucasian Americans drink significantly more soda on average than African Americans.

To test this hypothesis, we perform an independent samples t-test.

Group Statistics
ethnic orientation N Mean Std. Deviation Std. Error Mean
Average weekly consumption of soft drinks (12 oz cans) caucasian 364 9.90 9.049 .474
African-American 59 7.86 5.438 .708
Independent Samples Test
Levene’s Test for Equality of Variances t-test for Equality of Means
F Sig. t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference
Lower Upper
Average weekly consumption of soft drinks (12 oz cans) Equal variances assumed 2.167 .142 1.679 421 .094 2.037 -.347 4.421
Equal variances not assumed 2.390 117.957 .018 2.037 .349 3.724

The p-value for the Levene’s test for equality of variances of the samples is 0.142

Hence, we fail to reject the assumption of equality of variances of the two samples.

Assuming the equal variances of the average weekly consumption of soft drinks in Caucasian and African Americans, the p-value for the two-test t-test is 0.094

So, the p-value for the one-sided independent samples t-test that we have performed to test the null hypothesis is 0.094 / 2 = 0.047, which is statistically significant.

Hence, we reject the null hypothesis H0 against the alternate hypothesis H1.

Thus, we conclude that Caucasian Americans drink significantly more soda on average than African Americans.

(c)

%  of soft drinks consumed are favorite soft drink Stem-and-Leaf Plot

Frequency    Stem &  Leaf

4.00        0 .  0005

3.00        1 .  005

11.00        2 .  00000055555

9.00        3 .  000003344

16.00        4 .  0000000000000555

83.00        5 .  00000000000000000000000000000000000000000000000000000000000000000000000000000000005

34.00        6 .  0000000000000000000000000000000555

79.00        7 .  0000000000000000000000000005555555555555555555555555555555555555555555555555555

83.00        8 .  00000000000000000000000000000000000000000000000000000000000000000005555555555555599

92.00        9 .  00000000000000000000000000000000000000000000000000244455555555555555555555555555577788888899

52.00       10 .  0000000000000000000000000000000000000000000000000000

Stem width:    10

Each leaf:       1 case(s)

From the stem and leaf plot for the percentage of favorite soft drinks consumed, we observe that 341 people in the sample drink a simple majority (more than 50%) of their favorite drinks and 82 people in the sample drink 50% of their favorite drinks.

Hence, 341 people in the sample are brand loyal.

[2]

(a)

We want to test that the mean overall satisfaction and the mean “value of the Discover card” to customers are significantly above 3.5.

To test that the mean overall satisfaction is significantly above 3.5, we test the following hypothesis:

H0: The mean overall satisfaction is equal to 3.5

H1: The mean overall satisfaction is above 3.5

To test that the mean value of the Discover card is significantly above 3.5, we test the following hypothesis:

H0: The mean value of the Discover card is equal to 3.5

H1: The mean value of the Discover card is above 3.5

To test these two hypotheses, we perform one-sample t-test.

One-Sample Statistics
N Mean Std. Deviation Std. Error Mean
overall satisfaction 244 3.9877 1.00403 .06428
value of the card 244 3.3852 1.20661 .07725
One-Sample Test
Test Value = 3.5
t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference
Lower Upper
overall satisfaction 7.588 243 .000 .48770 .3611 .6143
value of the card -1.486 243 .139 -.11475 -.2669 .0374

The p-value of the one-sided t-test to test the hypothesis defined for the mean overall satisfaction is very low. So, we reject the null hypothesis that the mean overall satisfaction is equal to 3.5 against the alternate hypothesis that the mean overall satisfaction is above 3.5

Hence, we conclude that the mean overall satisfaction is significantly above 3.5

The p-value of the one-sided t-test to test the hypothesis defined for the mean value of the Discover card is 0.139 / 2 = 0.0695 which is more than 0.05. So, we fail to reject the null hypothesis that the mean value of the Discover card is equal to 3.5 against the alternate hypothesis that the mean value of the Discover card is above 3.5

Hence, we conclude that the mean value of the Discover card is not significantly above 3.5

(b)

We want to investigate if the likelihood of a person keeping the card related significantly more to the value they have for the card or to their satisfaction with the card and if the likelihood of a person recommending the card related more to its value or to the overall satisfaction perceived by the customer.

For this, we conduct paired sample t-test for the 4 pairs of responses.

Paired Samples Statistics
Mean N Std. Deviation Std. Error Mean
Pair 1 keeping card 4.2213 244 .81157 .05196
value of the card 3.3852 244 1.20661 .07725
Pair 2 keeping card 4.2213 244 .81157 .05196
overall satisfaction 3.9877 244 1.00403 .06428
Pair 3 recommending card 3.2582 244 1.12717 .07216
value of the card 3.3852 244 1.20661 .07725
Pair 4 recommending card 3.2582 244 1.12717 .07216
overall satisfaction 3.9877 244 1.00403 .06428
Paired Samples Correlations
N Correlation Sig.
Pair 1 keeping card & value of the card 244 .564 .000
Pair 2 keeping card & overall satisfaction 244 .584 .000
Pair 3 recommending card & value of the card 244 .632 .000
Pair 4 recommending card & overall satisfaction 244 .588 .000
Paired Samples Test
Paired Differences t df Sig. (2-tailed)
Mean Std. Deviation Std. Error Mean 95% Confidence Interval of the Difference
Lower Upper
Pair 1 keeping card – value of the card .83607 1.00501 .06434 .70933 .96280 12.995 243 .000
Pair 2 keeping card – overall satisfaction .23361 .84543 .05412 .12700 .34022 4.316 243 .000
Pair 3 recommending card – value of the card -.12705 1.00423 .06429 -.25368 -.00041 -1.976 243 .049
Pair 4 recommending card – overall satisfaction -.72951 .97320 .06230 -.85223 -.60679 -11.709 243 .000

The p-value for testing the equality of the responses – keeping the card and value of the card is extremely low, in the order of 10-29 whereas the p-value for testing the equality of responses – keeping the card and overall satisfaction is 0.000023

Hence, the likelihood of a person keeping the card is related significantly more to their overall satisfaction with the card than to the value they have for the card.

The p-value for testing the equality of the responses – recommending the card and value of the card is 0.049 whereas the p-value for testing the equality of responses – recommendingthe card and overall satisfaction is less than 0.001

Hence, the likelihood of a person keeping the card is related significantly more to the value they have for the card than to their overall satisfaction with the card.

(c)

We want to test if there is a significant difference between how consumer’s rate courtesy and friendliness of a customer service agent.

We want to test if there is asignificant difference between how consumers perceive professionalism and efficiency of handling the customer service call.

Finally, we want to test if there is a significant difference between the customer’s ratings of the rep’s concern for her needs and the reps’ ability to make the customer feel important.

So, there are 3 pairs of responses:

  • Courtesy and friendliness
  • Professionalism and efficiency
  • Concern and making feel important

For each of these three pairs, we need to test the following hypothesis:

H0: There is no difference between the ratings of the two responses of the pair.

H1: There is a difference between the ratings of the two responses of the pair.

To test these, we have to apply two-sided paired samples t-test for the 3 pairs of responses.

Paired Samples Statistics
Mean N Std. Deviation Std. Error Mean
Pair 1 courtesy 4.3730 244 .82418 .05276
friendliness 4.2254 244 .90858 .05817
Pair 2 professionalism 4.3852 244 .85053 .05445
efficiency 4.2828 244 .95039 .06084
Pair 3 concern 3.8484 244 1.19221 .07632
important feeling 3.3238 244 1.28848 .08249
Paired Samples Correlations
N Correlation Sig.
Pair 1 courtesy & friendliness 244 .750 .000
Pair 2 professionalism & efficiency 244 .628 .000
Pair 3 concern & important feeling 244 .646 .000
Paired Samples Test
Paired Differences t df Sig. (2-tailed)
Mean Std. Deviation Std. Error Mean 95% Confidence Interval of the Difference
Lower Upper
Pair 1 courtesy – friendliness .14754 .61760 .03954 .06966 .22542 3.732 243 .000
Pair 2 professionalism – efficiency .10246 .78157 .05004 .00390 .20102 2.048 243 .042
Pair 3 concern – important feeling .52459 1.04793 .06709 .39244 .65674 7.820 243 .000

For all of these two-sided paired two sample t-test, the p-values are less than 0.05 and are thus statistically significant.

Hence, the null hypothesis of no difference between the ratings of the two responses of the pair is rejected against the alternate hypothesis of significant difference between the ratings of the two responses of the pair for all the three pairs of responses.

So, we conclude that there is a statistically significant difference between how consumer’s rate courtesy and friendliness of a customer service agent.

We conclude that there is a statistically significant difference between how consumers perceive professionalism and efficiency of handling the customer service call.

We conclude that there is a statistically significant difference between the customer’s ratings of the rep’s concern for her needs and the reps’ ability to make the customer feel important.

It does not make sense to measure these three questions using two survey items each.