A math teacher claims that she has developed a review course that increases the

Question

A math teacher claims that she has developed a review course that increases the scores of students on the math portion of a college entrance exam. Based on data from the administrator of the exam, scores are normally distributed with =524. The teacher obtains a random sample of 2200 students, puts them through the review class, and finds that the mean math core of the 2200 students is 531 with a standard deviation of 117.

a) State the null and alternative hypotheses. Let be the mean score.

___ A. H0: <524, H1: >524

___ B. H0: =524, H1: >524

___ C. H0: >524, H1: 524

___ D. H0: =524, H1: 524

b) Test the hypothesis is at the =0.10 level of significance. Is a mean math score of 531 statistically significantly higher than 524? Conduct a hypothesis test using the P-value approach.

Find the test statistic. t0 = ___________ (round to two decimal places as needed)

Find the P-Value.

The P-value is _________. (round to three decimal places as needed)

Is the sample mean statistically significantly higher? ____ yes ____ no

c) Do you think that a mean math score of 531 versus 524 will affect the decision of a school admissions administrator? In other words, does the increase in the score have any practical significance?

____ no

____ yes, because every increase in score is practically significant

d) Test the hypothesis is at the =0.10 level of significance with n=400 students. Assume the sample mean is still 531 and the sample standard deviation is still 117. Is a sample mean of 531 significantly more than 524? Conduct a hypothesis test using the P-value approach.

Find the test statistic. t0 = ___________ (round to two decimal places as needed)

Find the P-Value.

The P-value is _________. (round to three decimal places as needed)

Is the sample mean statistically significantly higher?

____ yes

____ no

What do you conclude about the impact of large samples on the P-value?

___ A. As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences. ___ B. As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences. ___ C. As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically significant differences. ___ D. As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically significant differences.

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   524  
Ha:    u   >   524   [ANSWER, B]

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b)
              
As we can see, this is a    right   tailed test.      
              
df = n - 1 =    2199          
              
Getting the test statistic, as              
              
X = sample mean =    531          
uo = hypothesized mean =    524          
n = sample size =    2200          
s = standard deviation =    117          
              
Thus, t0 = (X - uo) * sqrt(n) / s =    2.806231651 [ANSWER, t0, test statistic]          

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Also, the p value is              
              
p =    0.002528302   [ANSWER, P VALUE]

*******************************

YES, IT IS SIGNIFICANTLY HIGHER. [ANSWER]

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C)      
              
I think 7 points is insignificant because the scores are in hundreds. So NO.

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d)

df = n - 1 =    399          
              
Getting the test statistic, as              
              
X = sample mean =    531          
uo = hypothesized mean =    524          
n = sample size =    400          
s = standard deviation =    117          
              
Thus, t0 = (X - uo) * sqrt(n) / s =    1.196581197 [ANSWER]          
              
Also, the p value is              
              
p =    0.116090173   [ANSWER]      
              
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As P > 0.10, NO, IT IS NO STATISTICALLY HIGHER.

***********************************

B. As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences. [ANSWER]

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