Question

Plant X is just like an ordinary plant in its infancy. After six months, however, there is a chance that it will develop a pink tint in all of its leaves.

Laura is an amateur biologist who loves the colour pink and has developed a particular chemical formula designed to increase the chances that Plant X will develop this tint after six months. In order to test whether this formula works, she sets up an experiment whereby 50 such plants are allowed to grow normally, and another 50 are given her special formula.

After a bit over six months, she records her observations in her diary. However, before she could do any testing on the data, her pet dog ate chunks out of her diary, leaving her with only a fraction of her initial observations. To make matters worse, her dog ate some of the plants as well!

The following data was all she could recover from the remnants of her diary:

	Normal	Formula	Total
No Tint	?	?	69
Pink Tint	?	?	?
Total	?	?	?
NB: results from the experiment show that exactly 40% of the plants developed a pink tint under normal circumstances!

Being knowledgeable in statistics and two-way tables, you offer to help her finish her experiment. Laura wishes to know the proportion of formula-administered plants that developed the pink tint. Calculate this proportion using all the data given. Give your answer as a whole percentage.

Proportion = %

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A survey asked a group of commuters from Dubai, Shanghai, and Paris what their primary mode of transport to work is. The results are tabulated in the two-way table below:

	Dubai	Shanghai	Paris
Metro/Train	182	180	159
Bus	157	102	120
Car	198	150	127
Other	185	184	168

Using SPSS and the data above, test whether there is any association between primary mode of transport and city of residence:

a)Calculate the chi-square test statistic (χ²). Give your answer to 3 decimal places.

χ² =

b)At α = 0.05, the null hypothesis of the chi-square test for association is rejectednot rejected.

Answer 1

Plant X is just like an ordinary plant in its infancy. After six months, however, there is a chance that it will develop a pink tint in all of its leaves.

Laura is an amateur biologist who loves the colour pink and has developed a particular chemical formula designed to increase the chances that Plant X will develop this tint after six months. In order to test whether this formula works, she sets up an experiment whereby 50 such plants are allowed to grow normally, and another 50 are given her special formula.

After a bit over six months, she records her observations in her diary. However, before she could do any testing on the data, her pet dog ate chunks out of her diary, leaving her with only a fraction of her initial observations. To make matters worse, her dog ate some of the plants as well!

The following data was all she could recover from the remnants of her diary:

	Normal	Formula	Total
No Tint	30	39	69
Pink Tint	20	11	31
Total	50	50	100
NB: results from the experiment show that exactly 40% of the plants developed a pink tint under normal circumstances!

Being knowledgeable in statistics and two-way tables, you offer to help her finish her experiment. Laura wishes to know the proportion of formula-administered plants that developed the pink tint. Calculate this proportion using all the data given. Give your answer as a whole percentage.

Proportion =(11/100)*100 = 11 %

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A survey asked a group of commuters from Dubai, Shanghai, and Paris what their primary mode of transport to work is. The results are tabulated in the two-way table below:

	Dubai	Shanghai	Paris
Metro/Train	182	180	159
Bus	157	102	120
Car	198	150	127
Other	185	184	168

Using SPSS and the data above, test whether there is any association between primary mode of transport and city of residence:

SPSS data is set up by weight command.

WEIGHT BY wt.

CROSSTABS

/TABLES=mode BY city

/FORMAT=AVALUE TABLES

/STATISTICS=CHISQ

/CELLS=COUNT

/COUNT ROUND CELL.

mode * city Crosstabulation
Count
		city			Total
		Dubai	Shanghai	Paris
mode	Metro	182	180	159	521
	Bus	157	102	120	379
	Car	198	150	127	475
	Other	185	184	168	537
Total		722	616	574	1912

Chi-Square Tests
	Value	df	Asymptotic Significance (2-sided)
Pearson Chi-Square	13.268a	6	.039
Likelihood Ratio	13.459	6	.036
Linear-by-Linear Association	.003	1	.954
N of Valid Cases	1912
a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 113.78.

Calculated chi square = 13.268, P=0.039 which is < 0.05 level of significance.

a)Calculate the chi-square test statistic (χ²). Give your answer to 3 decimal places.

χ² =13.268

b)At α = 0.05, the null hypothesis of the chi-square test for association is rejected.