Question

The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In 1996, 34% of students had not been absent from school even once during the previous school year. In a 2000 survey, responses from 8400 students showed that this figure had slipped to 33%. Oficials would, of course, be concerned if student attendance were decining. Do these figures give evidence of a change in student attendance? Complete parts a through e below. H 0

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:p=34%
H A
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:p
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=34%
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b) Check the assumptions and conditions The independence assumption justified: The randomization condtion is plausibly satisfied The 10% condition is plausibly satsfied. The successitalure condition satisfied c) Perform the test and find the P-vatue. The test statistic is z= (Round to two decimal placot as needed.)

Answer 1

To determine if there has been a change in student attendance, we can perform a hypothesis test. The test statistic can be calculated using the provided data, and the p-value can be determined from the standard normal distribution table or a calculator.

Step-by-step explanation:

To determine if there has been a change in student attendance, we can perform a hypothesis test. The null hypothesis (H0) is that the proportion of students not absent is still 34%, while the alternative hypothesis (HA) is that the proportion has changed from 34%.

Given that we have a large sample size (8,400 students) and proportions, we can use the normal approximation to perform the test. The test statistic can be calculated using the formula:

z = (p - p0) / sqrt(p0(1 - p0) / n),

where p is the sample proportion, p0 is the hypothesized proportion, and n is the sample size.

Using the given data, we can calculate the test statistic:

z = (0.33 - 0.34) / sqrt(0.34(1 - 0.34) / 8400) = -1.6528.

The p-value can be calculated using the standard normal distribution table or a calculator. From the table, the p-value is approximately 0.0987.