A survey was vadertakem to coaspare the educational background of several ditfer

Question

A survey was vadertakem to coaspare the educational background of several ditferent g each was asked to report the bighest level of completed edacation It was found that 218 of those suveyed tad coenpleted a Bachelors degree or higher generation. One generation of inherest was the Millennials (those born afer 1980). A sample of 660 Millennials was round the limits of your interval and ofali Mille nals hare eonpleted a Bohelor's degree or higher. Aner converting to percentages, with96% ccendence, we estimate between to two decimal places.) A sample of 679 Gen Xers (those born between 1965 & 1980, was takeo and they were asked the same question of this sample, i 671nd and % of sn Gen Xers have competed a nachelor's degree or higher I Aner eouverting to percentages, round the limits of your interval With 96% confidence, we esimate between to two decimal places.) Based cn the two intervals calculated, can we conclude there is a differesce in the percentage of indiniduals in these two generations who bave completed & Bachelor's degree ot higher? Tbe data cellected is incoacusive because the inervals etimaling the proportion who have completed a Rachelor's degree or higher for the two generations overlap O A larger percemage ot Millennials have completed a iacelors degree or higher becanew the upper lamit of the confidence interval for this group is greater than the upper linit of the coafidence interval for OA larger peronniage of Millensials have completed a Bachelor's degree ox higher because the entire inverval for this group exceeda the interval for the Gen Xers O A lacper percentage of Millennis's bave completed s Bacbelor's degree or thigher because most of the interval for this group exceods the interval for the Gen Xers Points possible: 10

Explanation / Answer

We have n = 660 and X = 218

Where X be the number of Millennials completed Bachelor's degree or higher

p = X / n = 218 / 660 = 0.33 that is 33% Millennials completed Bachelor's degree or higher

We solve this by using MINITAB

Choose Stat > Basic Statistics > 1 Proportion.

Choose Summarized data.

In Number of events, enter 218. In Number of trials, enter 660.

Click Options. Under Alternative, choose not equal to. Click OK in each dialog box.

96% Confidence interval for p is (0.292705, 0.367902)

therefore

With 96% confidence we estimate between 29% and 37% of all MIllennial have completed a Bachelor's degree or higher.

Now Part 2]

n = 679 and X = 167

Where X be the number of individuals completed Bachelor's degree or higher

p = X / n = 167 / 679 = 0.25 that is 25% individuals completed Bachelor's degree or higher

We solve this by using MINITAB

Choose Stat > Basic Statistics > 1 Proportion.

Choose Summarized data.

In Number of events, enter 167. In Number of trials, enter 679.

Click Options. Under Alternative, choose not equal to. Click OK in each dialog box.

96% Confidence interval for p is (0.212008, 0.279892)

therefore

With 96% confidence we estimate between 21% and 28% of all individuals have completed a Bachelor's degree or higher.

Part 3]

A large percentage of Millennials have completed a Bachelor's degree or higher because the entire interval for this group exceeds the interval for the Gen Xers.

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