Question

# (S 12.1) Suppose there is a random sample of n observations, divided into four groups. The...

(S 12.1) Suppose there is a random sample of n observations, divided into four groups. The table below summarizes the count of observations that were seen in each group.

 Group 1 Group 2 Group 3 Group 4 24 38 50 34

We are interested in testing the null hypothesis H0:p1=p2=p3=p4=0.25, against the alternative hypothesis HA:Atleastoneproportionisincorrect.

What is the expected count for each of the groups?

Expected:

What is the value of the test statistic? Round your response to at least 2 decimal places.

What are the appropriate degrees of freedom?

What is the P-value? Round to at least 4 decimal places

H0: p1 = p2 = p3 = p4 = 0.25

HA: At least one proportion is incorrect.

Level of significance = 0.05

Test statistic is

O: Observed frequency
E: Expected frequency.

E = n*pi

 O E (O-E) (O-E)^2 (O-E)^2/E 24 36.5 -12.5 156.25 4.280822 38 36.5 1.5 2.25 0.061644 50 36.5 13.5 182.25 4.993151 34 36.5 -2.5 6.25 0.171233 Total 146 9.51

Degrees of freedom = Number of E's - 1 = 4 - 1 = 3

P-value = P( ) = 0.0233

P-value < 0.05 we reject null hypothesis.

Conclusion:

At least one proportion is incorrect.

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