Homework SourseA manufacturer of highperformance automobiles produces disc
A manufacturer of high-performance automobiles produces disc brakes that must measure 322 millimeters in diameter. The department of quality control randomly draws 29 discs made by each of four production machines and measures their diameters.
This example uses the file brakes.sav . A nominal variable, Machine Number, identifies the production machine used to make the disc brake. Use One Sample t-test to determine whether or not the mean diameters of the brakes in each sample significantly differ from 322 millimeters. Because the data from each machine must be tested as a separate sample, the file must first be split into groups by the variable \"Machine Number\".
Table D1: One-Sample Statistics
Machine Number
N
Mean
Std. Deviation
Std. Error Mean
1
Disc Brake Diameter (mm)
29
322,007056
0,0135824
0,0025222
2
Disc Brake Diameter (mm)
29
321,995641
0,0143290
0,0026608
3
Disc Brake Diameter (mm)
29
322,007988
0,0228299
0,0042394
4
Disc Brake Diameter (mm)
29
322,001226
0,0102380
0,0019011
One-Sample Test
Machine Number
Test Value = 322
t-statistic
df
Sig. (2-tailed)
Mean Difference
90% Confidence Interval of the Difference
Lower
Upper
1
Disc Brake Diameter (mm)
2,797
28
0,009
0,0070558
0,002765
0,011346
2
Disc Brake Diameter (mm)
-1,638
28
0,113
-0,0043589
-0,008885
0,000167
3
Disc Brake Diameter (mm)
1,884
28
0,070
0,0079877
0,000776
0,015200
4
Disc Brake Diameter (mm)
0,645
28
0,524
0,0012262
-0,002008
0,004460
The SPSS output reports (for each of the 4 machines) the t-statistic, the p-value (named
\"Sig (two-tailed)\" in SPSS), the mean difference, X -o, (notice X bar- o) the square root of the sampling variance square root of S2 DIVIDE BYn (named std. error mean in SPSS) and the upper and lower bounds for the confidence interval. Use these data to solve the following problems for all 4 machines individually:
Questions:
a. Test H0: = 322 against H1: µ 322 on the 10% level (i.e. = 0.10) by comparing the t-statistic to the critical value. You should calculate the t-statistics by hand and check that SPSS provided the correct value of the t-statistics.
b. Test H0: = 322 against H1:µ 322 on the 10% level (i.e. = 0.1) by comparing the p-value (given in the table by SPSS) to .
Questions: 3A. the SPSS RESULT is below:
3a. At what measurement of scale (i.e. ratio, interval, ordinal or nominal scale) are the variables measured?
b. Are all three measures of central tendency relevant for all four variables?
c. Are measures of variability relevant for all three variables?
d. Are there missing data? If so, how many, and for which variables?
STATISTICS
Sex
Smoking frequency
Age
Age category
N
Valid
32374
14416
32374
32374
Missing
0
17958
0
0
Mean
1,57
2,07
46,36
2,57
Median
2,00
2,00
44,00
2,00
Mode
2
3
38
2
Std. Deviation
,495
,947
17,866
,918
Variance
,245
,897
319,211
,842
Range
1
2
67
3
Minimum
1
1
18
1
Maximum
2
3
85
4
FREQUENCY TABLE
Sex
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
man
13986
43,2
43,2
43,2
woman
18388
56,8
56,8
100,0
Total
32374
100,0
100,0
Smoking frequency
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
Every day
5999
18,5
41,6
41,6
Some days
1422
4,4
9,9
51,5
Not at all
6995
21,6
48,5
100,0
Total
14416
44,5
100,0
Missing
Refused
16
,0
Not ascertained
3
,0
Don\'t know
5
,0
System
17934
55,4
Total
17958
55,5
Total
32374
100,0
AGE CATEGORY
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
18-24
3484
10,8
10,8
10,8
25-44
13173
40,7
40,7
51,5
45-64
9537
29,5
29,5
80,9
65+
6180
19,1
19,1
100,0
Total
32374
100,0
100,0
e. Conduct an independent samples T-test to decide if the weight is equal between the two genders. Decide whether to assume equal variance or not. Use 5%-significance level for both decisions
T-TEST FROM SPSS
Group statistics
Sex
N
Mean
Std. Deviation
Std. Error Mean
Weight in kilos
man
13986
78,9916
6,91929
,05851
woman
18388
65,0113
6,31694
,04658
lndependent Sample test
Levene\'s Test for Equality of Variances
t-test for Equality of Means
F
Sig.
t
df
Sig. (2-tailed)
Mean Difference
Std. Error Difference
95% Confidence Interval of the Difference
Lower
Upper
Weight in kilos
Equal variances assumed
105,450
,000
189,255
32372
,000
13,98033
,07387
13,83554
14,12512
Equal variances not assumed
186,932
28595,831
,000
13,98033
,07479
13,83374
14,12692
| Table D1: One-Sample Statistics | |||||
| Machine Number | N | Mean | Std. Deviation | Std. Error Mean | |
| 1 | Disc Brake Diameter (mm) | 29 | 322,007056 | 0,0135824 | 0,0025222 |
| 2 | Disc Brake Diameter (mm) | 29 | 321,995641 | 0,0143290 | 0,0026608 |
| 3 | Disc Brake Diameter (mm) | 29 | 322,007988 | 0,0228299 | 0,0042394 |
| 4 | Disc Brake Diameter (mm) | 29 | 322,001226 | 0,0102380 | 0,0019011 |
Solution
