In 1974, only 6% of the students in the city school district were classified as being learning disabled.A school psychologist suspects that the proportion of learning-disabled children has increased dramatically over the years.To demonstrate this point, a random sample ofn = 200 students is selected.In this sample there are 24 students who have been identified as learning-disabled.You will use this information to determine if the sample indicates a change in the proportion of learning-disabled students at a 0.02 level of significance.

What is the hypothesized (assumed constant) population proportion for this test?

p=

(Report answer as a decimal accurate to 2 decimal places.Do not report using the percent symbol.)

Based on the researcher's understanding of the situation, how many tails would this hypothesis test have?

• one-tailed test
• two-tailed test

the correct pair of hypotheses for this situation: _________________________

The test statistic for this analysis is the sample count (i.e., the number of observed successes).What is this value?

k = __________

With these hypotheses, the p-value for this test is (assumingHois true) the probability of observing...

• at most 24 learning-disabled students
• at least 24 learning-disabled students
• more than 24 learning-disabled students
• at least 12 learning-disabled students

You are now ready to calculate the P-value for this sample. Be sure to use the (cumulative) binomial distribution to obtain an exact P-value.(Do not use the normal distribution as an approximation for the binomial distribution for this particular problem.)

P-value =

(Report answer as a decimal accurate to 4 decimal places.)

This P-value (and test statistic) leads to a decision to...

• reject the null
• accept the null
• fail to reject the null
• reject the alternative

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the proportion of learning-disabled students has increased.
• There is not sufficient evidence to warrant rejection of the claim that the proportion of learning-disabled students has increased.
• The sample data support the claim that the proportion of learning-disabled students has increased.
• There is not sufficient sample evidence to support the claim that the proportion of learning-disabled students has increased.