Question

Determining the target parameter. For each of the following studies, give the parameter of interest and state any assumptions that are necessary for the inferences to be valid.

a. Human Factors (December 2015) published a study on how well firefighter gloves fit. One objective was to compare the proportions of gloves that fit well for males and females. From data collected for 586 firefighters (546 males and 40 females), the researchers determined that 93% of males owned gloves that fit well, as compared to 49% of females a difference of 44%.

Short answer

a. The parameter of interest is,\({p_{male}} - {p_{female}}\).

Step-by-step solution

Given information

The total number of firefighters is 686.

The number of male firefighters is 546.

The number of female firefighters is 40.

The researchers determined that 93% of males owned gloves that fit well, as compared to 49% of females a difference of 44%.

State the condition required for valid large sample inference about \(\left( {{{\hat p}_1} - {{\hat p}_2}} \right).\)           \(\)

The condition required for valid large sample inference is given as follows:

• The two samples are randomly selected in an independent manner from the two target populations.
• The sample sizes \({n_1}\)and \({n_2}\)are both large so that the sampling distribution of \(\left( {{{\hat p}_1} - {{\hat p}_2}} \right)\) will be approximately normal.

State the parameter of interest and any assumptions that are necessary for the inferences to be valid.

Let \({p_{male}}\) be the proportions of gloves that fit well for males and \({p_{female}}\) be the proportion of gloves that fit well for females.

Therefore,

The parameter of interest is,\({p_{male}} - {p_{female}}.\).

i.e. The \({p_{male}} - {p_{female}}\)difference between the proportions of gloves that fit well for males and females.

In this study, the assumption that is necessary for the inference to be valid is that the samples are independent.