You have been asked by a men\'s clothing manufacturer, Nuke, to provide advice o
ID: 3341031 • Letter: Y
Question
You have been asked by a men's clothing manufacturer, Nuke, to provide advice on whether there is evidence of differences in the average heights of male citizens in three different countries. You have taken random samples of the heights of males (in cms) in those three countries and your data set is attached in csv delimited format (as a .txt file) using the link on the right.
Input the data set into SPSS and perform the appropriate analysis to answer the question above (marked in bold). Follow SPSS instructions to set up the data in the correct format. (You will need to create a new quantitative variable - with four decimals - with all the heights and a new quantitative variable with values 1, 2 or 3 depending on whether the men are from country 1, 2 or 3. Both of those variables have to be defined as "numeric" in SPSS.)
Choose the correct answer to the following questions, based on your results:
a) Based on the outputs from SPSS, and looking at the appropriate table, can the variances be pooled based on this data set?
A)Yes, because 1.503 is smaller than 2.306
B)Yes, because 2.226 is smaller than 2.306
C)Yes, because 1.503 is smaller than 2.226
D)No, because all standard deviations for the data set are different
b) Possible null and alternative hypothesis for the ANOVA test could include:
i)Ho: X1=X2=X3, where 1,2 and 3 refer to country 1, country 2 and country 3.
Ha: not all sample means are the same.
ii)Ho: 1=2=3, where 1,2 and 3 refer to country 1, country 2 and country 3.
Ha: not all sample means are the same.
iii)Ho: 1=2=3, where 1,2 and 3 refer to country 1, country 2 and country 3.
Ha: not all population means are the same.
iv)Ho: 1=2=3, where 1,2 and 3 refer to country 1, country 2 and country 3.
Ha: all population means are different.
The correct null and alternative hypothesis for the ANOVA test are: ????
c) Give the value of the test statistic to three decimal places:
d) Based on the ANOVA test, at the 1% significance level, we can (reject / fail to reject / accept) the null hypothesis.
e) Based on the ANOVA test, at the 1% significance level, we can conclude:
A)That the average heights of adult males in the three countries are all the same.
B)That the average heights of adult males in the three countries are not all the same.
C)That the average heights of adult males in the three countries are all different.
f) At the 1% significance level:
A)The average height of adult males in country 1 is significantly different from the average height of adult males in country 2.
B)The average height of adult males in country 1 is significantly different from the average height of adult males in country 3.
C)The average height of adult males in country 1 is significantly different from the average height of adult males in country 2 and in country 3.
Explanation / Answer
Result:
Descriptives
height
N
Mean
Std. Deviation
Std. Error
95% Confidence Interval for Mean
Minimum
Maximum
Lower Bound
Upper Bound
1.00
98
175.9693
1.15286
.11646
175.7382
176.2004
173.44
178.79
2.00
98
176.3929
1.50329
.15186
176.0915
176.6943
172.37
180.85
3.00
98
172.4094
1.30403
.13173
172.1480
172.6709
169.20
175.55
Total
294
174.9239
2.22558
.12980
174.6684
175.1793
169.20
180.85
ANOVA
height
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
938.205
2
469.103
266.058
.000
Within Groups
513.079
291
1.763
Total
1451.284
293
Test of Homogeneity of Variances
height
Levene Statistic
df1
df2
Sig.
2.204
2
291
.112
a) Based on the outputs from SPSS, and looking at the appropriate table, can the variances be pooled based on this data set?
A)Yes, because 1.503 is smaller than 2.306
Answer: B)Yes, because 2.226 is smaller than 2.306
C)Yes, because 1.503 is smaller than 2.226
D)No, because all standard deviations for the data set are different
b) Possible null and alternative hypothesis for the ANOVA test could include:
i)Ho: X1=X2=X3, where 1,2 and 3 refer to country 1, country 2 and country 3.
Ha: not all sample means are the same.
ii)Ho: 1=2=3, where 1,2 and 3 refer to country 1, country 2 and country 3.
Ha: not all sample means are the same.
iii)Ho: 1=2=3, where 1,2 and 3 refer to country 1, country 2 and country 3.
Ha: not all population means are the same.
iv)Ho: 1=2=3, where 1,2 and 3 refer to country 1, country 2 and country 3.
Ha: all population means are different.
The correct null and alternative hypothesis for the ANOVA test are: ????
Answer: iii)Ho: 1=2=3, where 1,2 and 3 refer to country 1, country 2 and country 3.
Ha: not all population means are the same.
c) Give the value of the test statistic to three decimal places:
F= 266.058
d) Based on the ANOVA test, at the 1% significance level, we can (reject / fail to reject / accept) the null hypothesis.
Reject the null hypothesis.
e) Based on the ANOVA test, at the 1% significance level, we can conclude:
A)That the average heights of adult males in the three countries are all the same.
Answer: B)That the average heights of adult males in the three countries are not all the same.
C)That the average heights of adult males in the three countries are all different.
f) At the 1% significance level:
A)The average height of adult males in country 1 is significantly different from the average height of adult males in country 2.
Answer: B)The average height of adult males in country 1 is significantly different from the average height of adult males in country 3.
C)The average height of adult males in country 1 is significantly different from the average height of adult males in country 2 and in country 3.
Descriptives
height
N
Mean
Std. Deviation
Std. Error
95% Confidence Interval for Mean
Minimum
Maximum
Lower Bound
Upper Bound
1.00
98
175.9693
1.15286
.11646
175.7382
176.2004
173.44
178.79
2.00
98
176.3929
1.50329
.15186
176.0915
176.6943
172.37
180.85
3.00
98
172.4094
1.30403
.13173
172.1480
172.6709
169.20
175.55
Total
294
174.9239
2.22558
.12980
174.6684
175.1793
169.20
180.85
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