SPSS Exercise
Comparing Means:
One or Two Samples t-Tests
t- Test and Z-Tests are commonly used for making comparisons between the means of the two samples or between some standard value and the mean of one sample.
One sample test:
A Business school in its advertisement claims that the average salary of its graduates in a particular lean year is at par with average salary offered at the top five business schools. A sample of 30 graduates from the business school, whose claim was to be verified, was taken at random. There salaries are given at random below:
Average salary in that year was 7, 50,000
H0: There is no difference between the average salary of the business school perceived and the average salary of the top five business schools.
Syntax Analyse-Compare means-one sample test Fill in test value as 750
Results:
One-Sample Statistics
N Mean Std.
Deviation Std. ErrorMean salary of the graduate student 30 713.50 81.26 14.84 One-Sample Test Test Value = 750 t df Sig.
(2-tailed) DifferenceMean Confidenc95% e Interval of the Difference Lower Upper salary of the graduate student -2.460 29 .020 -36.50 -66.84 -6.16
Result: Since the p value has come out to be .020 therefore the difference is significant to reject the null hypothesis.
Paired t-test
1. A corporate training institution claimed that its training program can greatly enhance the efficiency of the call centre employees. A big call centre sent some of its employees for the training program. The efficiency was measured by the no. of deals closed by each employee in a one month period. Data was collected for a one month period before sending the employees for the training program. After the training program the data was
again collected on the same program. After the training program, data was collected on the same employees for a month period.
Variables: Employee, before, after
H0: There is no significant diff between employees before and after the training program.
H1: There is sig diff between employees before and after the training program. Syntax:
Analyse-Compare means-paired sample t-test
Paired Samples Statistics
Mean N Std. Deviation Std. ErrorMean
Pair 1 before 40.70 20 4.318 .965
after 44.15 20 6.158 1.377
Paired Samples Correlations
N Correlation Sig.
Pair 1 before & after 20 .281 .230
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 before - after -3.450 6.452 1.443 -6.470 -.430 -2.391 19 .027
Since the p value is coming out to be .027 which is very much lower than .05 so the null hypothesis is rejected at 5% level of significance.
Independent sample test:
A study was conducted to compare the efficiency of the workers of the two mines, one with private ownership and other with government ownership. The researcher was of the view that there is no significant difference between the efficiency of the two. The tonnage of the minerals mined by a worker in one shift was chosen as a criteria to access its efficiency. 20 workers from private mines and 24 from government owned mines were selected and there average output per shift was recorded.
H0: average output of the workers from mine 1 equals to that of workers from mine 2. Ho: Average output of the workers from mine 1 differs to that of workers from mine 2.
syntax: Analyse-compare means- independent sample t-test
There will be two options in the next dialogue box
1. Grouping variable.(mine will be the grouping variable) 2. Test variable.(Out put)
Define groups: The other option available there is define groups, click of this and feed 1 in the first blank and 2 in the second. Click on continue and ok.
output:
Group StatisticsMINE N Mean Std.
Deviation Std. ErrorMean
1 20 42.55 5.48 1.23
2 24 39.04 2.79 .57
Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig.
(2-tailed)DifferenceMeanDifferenceStd. ErrorConfidenc95% e Interval of the Difference Lower Upper OUTPUT Equal variances assumed 15.990 .000 2.742 42 .009 3.51 1.28 .93 6.09 Equal variances not assumed 2.596 27.044 .015 3.51 1.35 .74 6.28
In this table we get results of two tests- Levene’s test for equality of variances and t-test for equality of means. The table contains two sets of analysis, the first one assuming equal variance in the two groups and the second one consisting unequal variances. The Levene’s test tells us which statistic to consider to analyse the equality means. It test the null hypothesis that the two groups have equal variances. A small value of significance (.000) associated with Levene’s test indicates that the two groups have unequal variances and the null hypothesis is rejected that the variances are equal. Therefore the statistics associated with equal variance is not assumed should be used fot t-test of equality of means.
The t-test p-value has come out to be 0.015 which indicate that null hypothesis is rejected at 5% level of sig. Where as the difference is not significant at 1% level of sig. so null hyp. is accepted.
To find out the significance of association between educational background of PGDBM students and their performance in terms of grade.
Both the variables are coded as ‘code’ and ‘grade code’ representing educational background and grade obtained. Educational background their codes are given below:
Educational Background Code B.com. 1 B.E. 2 B.Sc. 3 BBA. 4 B.A. 5
Grade codes are as follows: Grade obtained: grade code
A 1
B 2
C 3
These two variables cross tabulated for twenty five observations. A cross Tabulation with a chi-square test is performed
Syntax: Analyse- Descriptive- cross tabs- select one variable in row and the other one in column.
Case I
Armand’s Pizza Parlors is a chain of Italian Food restaurants located in a five state area. The most successful locations for Armand’s have been near college campuses. The manager believes that the quarterly sales of these restaurants (denoted by Y) are related positively to the size of the student population (denoted by X); that is the restaurant near campuses with a large population tend to generate more sales than those located near campuses with a small population. Use regression analysis to predict the sale of restaurant for a given data of 16000 students.
Student’s population and quarterly sales data for 10 Armand’s Pizza Parlors
Case II
The owner of the pizza Corner Bangalore would like to build a regression model
consisting of six factors to predict the sale of pizza. Data for the past 15 months on sales and six different factors were collected for the purpose.
Input:
Dependent variables: Y=Monthly sales in rs. Independent variables: X1= No. of delivery boys. X2=Cost of ad in Rs. X3=No. of out lets X4=Variety of pizza’s
X5=Competitors activity index X6=No. of existing customers (‘000)
This problem relates to the taste and quality of food served to 28 customers in TAJ Group of Hotels chain. The customers, who are basically from the higher income group (HIG), were asked to give their opinion about the quality/ taste of the four common non
vegetarian dishes served to them. The analysis of the problem gives us the variance between the dependent variable (rating) and the independent variable (Non Veg Dishes) The following are the common dishes served at the above hotel’s chain restaurant are coded as follows:
CODE: DISH NAME
1 Chicken platter
2 Honey chicken
3 Chicken spinach
4 Tandoori Chiken
In This problem we have to consider the four different non vegetarian dishes that are being offered by TAJ Group of hotels chain. The hotel group wants to test, which of the above mentioned dishes is being preferred by the target customers, that is HIG
Customers. At random these 28 respondents were asked for their preference on a scale of 10. (1-not liked at all and 10 is most preferred dish).
Factor analysis
Private domestic airline operators raised their airfare in December 2000. Indian Airlines, the government-owned carrier, was the only domestic airline which did not follow suit. Information available (source-Economic Times) showed that people still prefer to fly Jet Airways. Our group set out to ascertain the reasons for the above preference, as according to Indian Airlines officials domestic flyers are price-conscious customers.
Our study consisted of 20 respondents who had recently flown with Jet Airways. They were asked to indicate on a seven point scale (1 = completely agree, 7 = completely disagree), their agreement or disagreement with the set of 10 statements relating to their perceptions and attributes of the airline.
The 10 statements were as follows:
1. They (Jet Airways) are always on time. 2. The seats are very comfortable.
3. I love the food they provide.
4. Their air-hostesses are very beautiful. 5. My boss/friend flies with the same airline. 6. The airlines have younger aircrafts.
7. I get the advantage of a frequent flyer program. 8. It (the flight timing) suits my schedule.
9. My mom feels safe when I fly Jet.
