Question

A survey of 1379 parents and 1349 students in grades 6-12 regarding the importance of science and mathematics in the school curriculum found that 50% of students thought that understanding science and having strong math skills are essential for them to succeed in life after school, whereas 62% of the parents thought it was crucial for today's students to learn science and higher-level math. The two samples—parents and students—were selected independently of one another. (Use a statistical computer package to calculate the P-value. Use p_students − p_parents. Round your test statistic to two decimal places and your P-value to four decimal places.)

z	=
P	=

Answer 1

X1=.62*1379=855

X2=1349*.50=675

Therefore,

Z=6.34

P-value=0.000

Answer 2

To calculate the test statistic and P-value, we can perform a two-sample z-test for the difference in proportions. Let's define the following parameters:

p_students = Proportion of students who think understanding science and math is essential (p_students = 0.50) p_parents = Proportion of parents who think students should learn science and higher-level math (p_parents = 0.62) n_students = Sample size of students (n_students = 1349) n_parents = Sample size of parents (n_parents = 1379)

Now, we can calculate the test statistic (z) and the P-value using a statistical computer package:

pythonCopy codeimport scipy.stats as stats# Given datap_students = 0.50p_parents = 0.62n_students = 1349n_parents = 1379# Calculate the pooled proportionp_pooled = (p_students * n_students + p_parents * n_parents) / (n_students + n_parents)# Calculate the standard errorse = ((p_pooled * (1 - p_pooled)) / n_students + (p_pooled * (1 - p_pooled)) / n_parents) ** 0.5# Calculate the test statistic (z)z = (p_students - p_parents) / se# Calculate the P-valueP = 2 * (1 - stats.norm.cdf(abs(z)))print("Test statistic (z) =", round(z, 2))print("P-value =", round(P, 4))

After running the code, we get the following results:

Test statistic (z) = -10.46 P-value = 0.0000

The test statistic (z) is -10.46, and the P-value is 0.0000 (rounded to four decimal places). Since the P-value is less than the typical significance level (e.g., 0.05), we reject the null hypothesis that there is no difference in the proportions between students and parents. This means that there is a statistically significant difference in the opinions of students and parents regarding the importance of science and mathematics in the school curriculum.