A researcher classifies firefighters according to whether their gloves fit well or poorly and by gender....

A researcher classifies firefighters according to whether their gloves fit well or poorly and by gender. They want to know if there is a difference in the proportion of poorly fitted gloves and gender. At alpha = 0.01, use the chi-square test to determine if there is a difference in the population proportion of glove fitness for the two genders. Using the observed data in the table, determine the percentage of gloves that fit poorly for each gender (fit poorly/total). Which gender has higher percentage of poorly fit gloves? Why?

Observed data	Males	Females	Total
Gloves fit poorly	132	20	152
Gloves fit well	415	19	434
Total	547	39	586
Expected data	Males	Females	Total
Gloves fit poorly
Gloves fit well
Total

Expert Solution

	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	Males	Females	Total
Gloves fit poorly	547*152/586=141.884	39*152/586=10.116	152
Gloves fit well	547*434/586=405.116	39*434/586=28.884	434
Total	547	39	586

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   13.9691

Level of Significance =   0.01
Number of Rows =   2
Number of Columns =   2
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 2- 1 ) =   1

p-Value =   0.0002   [Excel function: =CHISQ.DIST.RT(χ²,df) ]
Decision:    p-value < α , Reject Ho

conclusion: there is a difference in the population proportion of glove fitness for the two genders

=============

percentage of gloves that fit poorly for male=132/547=24.13%

percentage of gloves that fit poorly for female=20/39=51.28%

Female gender has higher percentage of poorly fit gloves

orchestra answered 1 year ago

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