Exercise Problem In 1978, only 9% of the students in the city school district we

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Exercise Problem
In 1978, only 9% 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 of n=400students is selected. In this sample there are 55 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 0.01 level of significance.

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

1one-tailed test

2two-tailed test

Choose the correct pair of hypotheses for this situation:

(A)

(B)

(C)

(D)

(E)

(F)

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

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

1at most 55 learning-disabled students

2at least 55 learning-disabled students

3more than 55 learning-disabled students

4at least 36 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...

1reject the null

2accept the null

3fail to reject the null

4reject the alternative

As such, the final conclusion is that...

1There is sufficient evidence to warrant rejection of the claim that the proportion of learning-disabled students has increased.

2There is not sufficient evidence to warrant rejection of the claim that the proportion of learning-disabled students has increased.

3The sample data support the claim that the proportion of learning-disabled students has increased.

4There is not sufficient sample evidence to support the claim that the proportion of learning-disabled students has increased.

(A) (B) (C) H0:p=0.09H0:p=0.09
Ha:p<0.09Ha:p<0.09 H0:p=0.09H0:p=0.09
Ha:p0.09Ha:p0.09 H0:p=0.09H0:p=0.09
Ha:p>0.09Ha:p>0.09 (D) (E) (F) H0:p=0.138H0:p=0.138
Ha:p<0.138Ha:p<0.138 H0:p=0.138H0:p=0.138
Ha:p0.138Ha:p0.138 H0:p=0.138H0:p=0.138
Ha:p>0.138Ha:p>0.138

Explanation / Answer

What is the hypothesized (assumed constant) population proportion for this test? =0.09

Based on the researcher's understanding of the situation, how many tails would this hypothesis test have? 1 tailed

option C

H0:p=0.09
Ha:p>0.09

The test statistic for this analysis is the sample count (i.e., the number of observed successes). What is this value? =55

P-value = 1-binomdist(54,400,0.09,false) =0.0012

This P-value (and test statistic) leads to a decision to... 1reject the null

As such, the final conclusion is that...

3The sample data support the claim that the proportion of learning-disabled students has increased.

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