Mathematics, 19.12.2019 23:31 ahrensy8444

Each person in random samples of 227 male and 293 female working adults living in a certain town in canada was asked how long, in minutes, his or her typical daily commute was. (use a statistical computer package to calculate the p-value. use μmales − μfemales. round your test statistic to two decimal places, your df down to the nearest whole number, and your p-value to three decimal places.)

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Answer from: rocksquad9125

the 95% confidence interval would be given by $-1.882 \leq \mu_{males} -\mu_{fmales} \leq 6.482$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X_1 =30.2$ represent the sample mean 1 (males)

$\bar X_2 =27.9$ represent the sample mean 2 (females)

n1=227 represent the sample 1 size (males)

n2=293 represent the sample 2 size (females)

s_1 =24 sample standard deviation for sample 1 (males)

s_2 =24.3 sample standard deviation for sample 2 (females)

$\sigma =3$ represent the population standard deviation

$\mu_1 -\mu_2$ parameter of interest.

Confidence interval

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{(\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2})}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =30.2-27.9=2.3$

Since the sample size is large enough we can assume that th t distirbution is approximately equal to the normal distribution in order to find the quantile.

Let's assume a Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$