Question

In two common species of flowers, a and b, the proportions of flowers that are blue are pa and pb , respectively. Suppose that independent random samples of 50 species-a flowers and 100 species-b flowers are selected. Let pˆa be the sample proportion of blue species-a flowers and pˆb be the sample proportion of blue species-b flowers. What is the mean of the sampling distribution of pˆa−pˆb ?.

Answer 1

The mean of the sampling distribution is ${p_{a}}-p__b}$

The mean of a sampling distribution is the population mean from which values are sampled. For a population of mean μ, the mean of the sampling distribution is $\mathbf{ \mu_x}$

∴

$\mathbf{\mu_x = \mu}$

From the parameters given:

• Suppose that independent random samples of 50 species-a flowers
• and 100 species-b flowers are selected

where;

• $\mathbf{\hat p_a}$ = sample proportion of blue specie-a
• $\mathbf{\hat p_b}$ = sample proprotion of blue specie-b

The mean of the sampling distribution of $\mathbf{\hat p_a -\hat p_b}$ is ${p_{a}}-p__b}$

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