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 mu equals515. The teacher obtains a random sample of 2000 students, puts them through the review class, and finds that the mean math score of the 2000 students is 520 with a standard deviation of 117. Complete parts (a) through (d) below. (a) State the null and alternative hypotheses. Let mu be the mean score. Choose the correct answer below. A. Upper H 0 : mu greater than 515, Upper H 1 : mu not equals 515 B. Upper H 0 : mu equals 515, Upper H 1 : mu not equals 515 C. Upper H 0 : mu equals 515, Upper H 1 : mu greater than 515 D. Upper H 0 : mu less than 515, Upper H 1 : mu greater than 515 (b) Test the hypothesis at the alpha equals0.10 level of significance. Is a mean math score of 520 statistically significantly higher than 515? Conduct a hypothesis test using the P-value approach. Find the test statistic. t 0equals nothing (Round to two decimal places as needed.) Find the P-value. The P-value is nothing. (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 520 versus 515 will affect the decision of a school admissions administrator? In other words, does the increase in the score have any practical significance? No, because the score became only 0.97% greater. Yes, because every increase in score is practically significant. (d) Test the hypothesis at the alphaequals0.10 level of significance with nequals400 students. Assume that the sample mean is still 520 and the sample standard deviation is still 117. Is a sample mean of 520 significantly more than 515? Conduct a hypothesis test using the P-value approach. Find the test statistic. t 0equals nothing (Round to two decimal places as needed.) Find the P-value. The P-value is nothing. (Round to three decimal places as needed.) Is the sample mean statistically significantly higher? No Yes 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 significant differences. B. As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically significant differences. C. As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences. D. As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences. Click to select your answer(s).

Answer #1

Ans:

a)

H 0 : mu equals 515,

H 1 : mu greater than 515

b)alpha=0.1

critical z value=1.282

Test statistic:

t=(520-515)/(117/SQRT(2000))

t=1.91

p-value=0.028

Reject the null hypothesis,as p-value<0.1

**Yes**

c)yes, because every increase in score is practically significant.

d)

t=(520-515)/(117/SQRT(400))

t=0.85

p-value=0.197

**No**,not significant.

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

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