Using the data below, carry out an hypothesis test to determine whether ....?

Question

there is an association between the colour of olives preferred by respondents and the region in which they live. State your conclusion clearly

Region ....black olives green olives Total
West .......65 .................53 ................118
East ........59 .................76 ................135
South ......48 .................42 ................90
Total .......172 ..............171 ..............343

Answer 1

Use Chi-Square (Excel has this particular function)
row = 3, col = 2
p-value = .153
degree of freedom = (3-1)(2-1) = 2(1) = 2
X^2 computed = 3.76
p (level of significance) = .05
X^2 critical = 5.99
Since X^2 comp < X^2 crit, The null hypothesis is accepted.
Conclusion: There is no association between the colour of olives preferred by the respondents and the region in which they live.

Answer 2

I would say there is by far the highest number of respondents in West, followed by East and South, by olive breakdown according to colour but in sum Totals the highest figure is for East, then, West and again, South.

Based on the above surmise, it can be seen from Total that of 343 surveyed, approx. half (172) love black olives and the remainder, also half (171), love green olives. Fair enough. But breaking this down, now, by Region to conclude that 17 % and 22 % in East accounting for 135 of 343 (39 %) of black and green olives lovers respectively. Next biggest group, West, with 118 of 343 (or 34 % overall) breaks down to 19 % who love black olives and 15 % who prefer green olives.

Finally is 26% of South made up of 14 % black olives lovers and 12 % who prefer green olives.

Answer 3

Assuming the data collection is unbiased....
H0: The preferrence is independent of region
HA: The preference depends on region
You need an alpha = level of significance.
The obvious choice is a X^2 (chi-square) test with df = (rows - 1)*(cols - 1) = 2 * 1 = 2.
The test stat is the sum of (observed - expected)^2/expected over the 6 cells. (To find expected values, multiply the total for the row times the total for the column and divide by the overall total - so the expected value for west/black is 118*172/343 = 59.172). You then compare the test stat to the value in the chi square table corresponding to df = 2 and the chosen alpha. If the test stat is >= table value, choose the alternate.

Answer 4

In order to arrive at any conclusion from the data presented it is necessary to make some assumptions ..


1) The conditions of the survey were identical in each Region (same staff asked the exact same questions in the exact same circumstances)
... you have to eliminate any possibility that the respondents choice was dependent on who asked the question, when they were asked and the way they were asked ... (eg. green olives might be more popular in the morning and black ones more popular if asked in the rain - and some respondents might simply choose the first one presented to them, especially since they were all forced to make a choice (i.e. no-one was allowed to respond "no preference")

2) Other than the region in which they live, all respondents are identical .. (nationality, origin, age, sex,education, upbringing, income etc etc)
... you have to eliminate the possibility that the respondents made personal choices dependent on factors such as what they were fed at school, what their parents eat, what their friends eat etc.

3) The historical type, availability & pricing of Olives in each region has been identical for the entrire life time of each of the respondants to date
.. plainly if one type of olive has been in short supply and/or has been considerably more expensive during the upbringing of the respondants, this will bias their response


Needless to say, since it is impossible to eliminate bias, it is impossible to reach any conclusion ... especially on the tiny sample size and tiny differences indicated.

Answer 5

In the West 55% prefer black olives
In the East 44% prefer black olives
In the South 53% prefer black olives

Answer 6

Read Dr Octavian answer!

Answer 7

FIRSTLY YOU ARE MEANT TO MAKE AN HYPOTHESIS BEFORE YOU COLLECT YOUR DATA AND SECONDLY ARE YOU SURE YOU WANT A HYPOTHESIS OR DO YOU REALLY WANT A CONCLUSION?????????