Statistics Homework: Chi-Square Test Solutions for Week 8 Exercises

This document presents solutions to a statistics homework assignment, specifically addressing chi-square tests. The solutions include calculations for chi-square statistics, p-values, and confidence intervals for various scenarios. The assignment involves interpreting results, such as determining whether to reject or fail to reject null hypotheses based on the level of significance and p-values. The document also includes analyses of different datasets related to topics like personality preferences, and variance in annual wheat production. Furthermore, it provides insights into understanding the relationship between observed and expected frequencies, and the implications of these relationships in statistical analysis.

STATISTICS
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Question 8
(b) Chi square stat = 0.803
(c) p value = 0.938 (Option a) P-value > 0.100
(d) (Option a) Since the P-value > α, we fail to reject the null hypothesis.
(e) (Option a) At the 5% level of significance, the evidence is sufficient to conclude that the
natural distribution of browse does not fit the feeding pattern.
Question 11
(b) Chi square stat = 30.67
(c) p value = 0.240 (Option a) P-value > 0.100
(f) 95% confidence interval: Lower limit = 30.95, Upper limit = 93.72
Option (c) We are 95% confident that σ lies within this interval.
Question 12
(b) Chi square stat = 29.25
(c) p value = 0.0223 (Option d) 0.010 < P-value < 0.025
(f) 95% confidence interval: Lower limit = 47.76, Upper limit = 199.43
Question 13
(b) Chi square stat = 6.42
(Option d) We assume a normal population distribution.
(c) p value = 0.998 (Option a) P-value > 0.100
(d) Option b (Since the P-value > α, we reject the null hypothesis.)
(e) Option b (At the 5% level of significance, there is sufficient evidence to conclude that the
new typhoid shot has a smaller variance of protection times.)
(f) 90% confidence interval: Lower limit = 1.84, Upper limit = 5.33
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Question 14
(d) Option c, Since the P-value ≤ α, we reject the null hypothesis.
(f) 95% confidence interval: Lower limit = 295.70, Upper limit = 2083.03
Question 16
(a) Option c
(C) P value = 0.01311 (Option d) 0.010 < p-value < 0.025
(d) Option c (At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data
are not statistically significant.)
(e) Option d (Fail to reject the null hypothesis, there is insufficient evidence that the variance
in annual wheat production is greater in the first plot.)
Question 19
(c) Option (a) P-value > 0.200
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