3. Another item in the ACME Jet Propelled Line of products is the ACME Jet Propelled...

3. Another item in the ACME Jet Propelled Line of products is the ACME Jet Propelled Unicycle, which even the most unbalanced individual can ride with ease. The most popular colors for ACME Jet Propelled Unicycles were white, 30%, black, 17%, red, 14%, yellow, 12%, green, 11%, blue 8%, and other, 8%. The following table presents the results of a survey of randomly selected ACME Jet Propelled Unicycle owners in a particular desert area revealed the follwoing.

Color White(45) Black(32) Red(30) Yellow(30) Green(22) Blue(15) Other(6) Owned

At a 5% level of significance, do the proportions differ from those stated?.

State the null and alternative hypotheses.

Answer:
State the hypothesis test that you are using for the situation.

c. Is this a left-tailed, right-tailed, or two-tailed test?

Find the p-value. Round to four decimal places.
What is the decision about H0?

Answer:

Answer:f. Interpret the decision to write a conclusion for the test.

Answer:

Solutions

Expert Solution

Hypothesis:

H0: Proportion of colors are same as stated.

Ha: Proportion of colors differ from those stated.

We use chi-square goodness of fit test for testing this hypothesis.

Chi-square test is always right tailed test.

Observation Table:

Color	Oi	Pi	Ei=Npi	(Oi-Ei)2/Ei
White	45	0.3	54	1.5
Black	32	0.17	30.6	0.064052
Red	30	0.14	25.2	0.914286
Yellow	30	0.12	21.6	3.266667
Green	22	0.11	19.8	0.244444
Blue	15	0.08	14.4	0.025
Other	6	0.08	14.4	4.9
	N = 180			10.91445

Test statistic,

Degrees of freedom = n-s-k-1 = 7-0-0-1=6

Where,

n = Total number of observations

s = number of parameter estimated

k= number of degrees of freedom lost due to pooling

P-value = 0.0911. It is obtained using Excel with function =CHIDIST(10.9145,6)

Since p-value is greater than 0.05, hence we accept null hypothesis at 5% level of significance and conclude that Proportion of colors are same as stated.

orchestra answered 1 year ago

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