Subject: Mathematics    / Statistics
Question

According to the 2015 National Assessment of Education Progress (NAEP), 44% of high school seniors in the U.S. would like to have a job that involves using science. A researcher believes that the proportion of high school seniors who would like to have a job that involves using science is higher for Ann Arbor high school seniors. To put his theory to the test (H0: p = 0.44 vs Ha: p > 0.44, where p represents the population proportion of all Ann Arbor high school seniors who would like a job involving science), the researcher takes a random sample of 284 Ann Arbor high school seniors, and 139 reported they would like to have a job that involves using science.

Assuming that the 284 responses from Ann Arbor high school seniors can be considered a random sample, check the remaining condition that is needed in order to conduct a large sample z test of the hypotheses. Make sure to include relevant formulas with correct notation and calculations.

Compute the observed z test statistic value. Make sure to include relevant formulas with correct notation. (State your result to at least two decimal places.)

Find the corresponding p-value for this test. Include a complete sketch or graph of the p-value as part of your work, shading the p-value area and labeling the distribution and x axis.

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