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?

Options:

Yes, because 1.206 is smaller than 2.070

Yes, because 2.409 is smaller than 2.070

Yes, because 1.035 is smaller than 2.206

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: μ₁=μ₂=μ₃, where 1,2 and 3 refer to country 1, country 2 and country 3.
Ha: not all sample means are the same.

iii)Ho: μ₁=μ₂=μ₃, where 1,2 and 3 refer to country 1, country 2 and country 3.
Ha: not all population means are the same.

iv)Ho: μ₁=μ₂=μ₃, 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: iiiiiiiv

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 rejectfail to rejectaccept the null hypothesis.

e) Based on the ANOVA test, at the 1% significance level, we can conclude:

That the average heights of adult males in the three countries are all the same.

That the average heights of adult males in the three countries are not all the same.

That the average heights of adult males in the three countries are all different.

f) At the 1% significance level:

The average height of adult males in country 1 is not significantly different from the average height of adult males in country 2.

The average height of adult males in country 1 is not significantly different from the average height of adult males in country 3.

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.

Data:

Country1,Country2,Country3
170.1014,172.416,174.3598
170.015,171.8691,175.4298
167.1165,172.0095,175.8213
170.7974,172.8481,175.2108
167.4691,171.0614,177.1758
167.3169,173.8291,174.3697
170.1959,172.9586,174.2155
168.9618,173.939,173.0001
170.5938,173.4236,176.1926
170.9124,173.6931,176.1405
171.1293,171.3203,175.0041
169.2706,171.8757,176.1782
170.6393,172.5636,175.3204
170.2208,173.2316,175.4489
171.0913,174.4545,175.2355
170.7434,172.752,175.6279
171.1775,174.6139,175.222
169.9417,173.6705,178.4448
169.9234,174.5089,173.7
171.3093,173.2523,172.8748
167.5516,172.3118,173.7312
169.4945,171.3223,173.788
168.5753,173.2866,174.5797
169.6409,174.0823,174.8978
170.8784,172.7489,174.8378
171.0909,172.4511,175.7496
168.8821,172.7296,175.5671
169.5347,171.7841,176.0015
170.2644,172.5084,177.2339
169.7498,172.8831,176.5677
170.4622,173.155,173.5601
170.5799,173.0235,172.3053
168.984,173.8336,176.1823
169.8878,173.2312,172.8972
167.5415,175.2768,175.1801
171.4744,173.4744,175.1426
169.3451,175.2654,177.7726
168.6554,172.2323,175.0169
169.7953,173.7319,174.4912
168.3856,172.7877,175.383
170.075,173.8202,175.395
169.4272,173.8127,175.1841
172.7133,170.4768,174.3697
171.4662,171.5075,173.6329
167.1037,171.3708,175.4798
170.6296,173.5822,173.4886
168.4222,174.8642,173.8614
169.7939,172.7078,176.6975
170.2973,174.0748,174.5973
170.9973,173.7546,174.9316
169.7723,171.838,176.1798
171.9916,173.577,174.7399
169.5229,172.1977,176.3352
170.493,174.9195,174.6859
170.8977,173.0609,176.3154
170.2022,175.0632,175.8552
171.1571,172.5899,174.8444
170.4879,173.8073,174.0612
169.159,173.0247,173.8483
167.9336,170.6736,174.7759
172.3303,171.9214,174.5742
169.3746,173.835,174.6096
170.224,173.0341,176.2803
170.7758,171.7575,174.7428
170.2363,172.3483,176.4724
169.0143,173.3994,174.4621
169.5387,171.9084,176.2671
169.9501,174.2699,174.4733
171.8748,172.3311,175.3119
169.067,175.2706,176.2649
171.0416,171.8042,174.6032
170.4703,173.339,174.5741
169.8194,171.2748,177.5041
168.8316,172.2316,176.2412
169.759,172.3881,174.5816
169.996,173.5816,175.8787
168.3367,174.2306,174.6679
170.3306,173.4606,175.9471
169.1132,172.6523,176.799
169.9869,174.0786,173.1746
170.5035,174.0587,176.3346
169.0144,173.2442,176.8496
169.7541,173.7855,175.157
170.5201,173.5954,177.1955
167.897,171.9156,175.2865
171.3432,174.0115,173.6155
173.0094,172.3114,172.4678
171.2513,172.3753,174.6999
169.7211,173.3123,175.9563
170.6143,172.731,175.4809
168.8568,172.9418,175.5963
172.3534,173.8144,174.4075
171.2288,174.3562,175.2728
171.0448,172.8624,173.1336
169.049,173.4932,174.1879
170.4839,172.814,174.1174
169.43,173.3755,175.7237
169.7263,173.628,175.083

Answer 1

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