Question

aoston #3a: The National Center for Education Statistics monitors marw aspects of elementary and secondary monitors many numbers are often used as a baseine to assess change. In 1996, 34% of students had 8302 randomly selected students showed that this fig atendance has dropped? even once during the previous month. In the 2000 survey, responses from ure had slipped to 33%. Can we conclude that the number of students with perfect a) State the Null and Alternative Hypotheses b) Write and Check the assumptions and conditions c) Assuming all assumptions and conditions are met, perform the appropriate hypothesis test. Show all work. Explain. d) What is your conclusion using a significance level of 0.05.

Answer 1

(a)

H0: Null Hypothesis: P $\geq$ 0.34

HA: Alternative Hypothesis: P < 0.34

(b) Assumptions and conditions:

(i) The sampling method is Simple Random Sampling

(ii) Each sample point can result in just two outcomes.

(iii) The sample includes at least 10 successes and 10 failures

(iv) The population size is at least 20 times as big as the sample size.

(c) Q = 1 - P = 0.66

n = 8302

p = 0.33

SE = $\sqrt{PQ/n}$

$=\sqrt{0.34\times 0.66/8302}=0.0052$

Test statistic is given by:
Z = (p - P)/SE

= (0.33 - 0.34)/0.0052 = - 1.9231

$\alpha$ = 0.05

One Tail - Left Side Test

From Table, critical value of Z = - 1.645

Since the calculated value of Z = - 1.9231 is less than critical value of Z = - 1.645, Reject H0.

(d) Conclusion;

The data support the claim that the number of students with perfect attendence has dropped.