Question

In: Statistics and Probability

the average scores of math students in a certain school is 75 with a standard deviation...

the average scores of math students in a certain school is 75 with a standard deviation of 8.1. one hundred students were randomly selected, and the average score was found to be 71. the director wants to know wether students have deteriorated. significance level is 0.01

1) the hypotheses are ?

2)Decision and conclusion ?

3) the critical value is ?

4) the test statistic is ?

Expert Solution

Solution :

The null and alternative hypothesis is ,

H0 : = 75

Ha : 75

Test statistic (t) =

= ( - ) / s / n

= (71 - 75) / 8.1 / 100

Test statistic = -4.94

P-value = 0

= 0.01

P-value <

Reject the null hypothesis .

There is sufficient evidence to support the claim.

orchestra answered 2 years ago

A math professor claims that the standard deviation of IQ scores of the students majoring in...

A math professor claims that the standard deviation of IQ scores of the students majoring in mathematics is different from 15, where 15 is the standard deviation of IQ scores for the general population. To test his claim, 10 students were surveyed and their IQ scores were recorded. 120, 110, 113, 123, 119, 160, 220, 119, 110, 140 Test the professor’s claim using a 0.01 level of significance.

What is the standard deviation of students math test scores? 12 18 27 31 40 42...

What is the standard deviation of students math test scores? 12 18 27 31 40 42 14 20 27 32 40 51 14 20 27 32 40 56 14 21 29 32 40 60 16 23 31 36 40 65

The test scores for a math exam have a mean of 72 with a standard deviation...

The test scores for a math exam have a mean of 72 with a standard deviation of 8.5. Let the random variable X represent an exam score. a) Find the probability that an exam score is at most 80. (decimal answer, round to 3 decimal places) b) Find the probability that an exam score is at least 60. (decimal answer, round to 3 decimal places) c) Find the probability that an exam score is between 70 and 90. (decimal answer,...

A certain test preparation course is designed to improve students' SAT Math scores. The students who...

A certain test preparation course is designed to improve students' SAT Math scores. The students who took the prep course have a mean SAT Math score of 526, while the students who did not take the prep course have a mean SAT Math score of 515. Assume that the population standard deviation of the SAT Math scores for students who took the prep course is 44.6 and for students who did not take the prep course is 45.2. The SAT...

The state average for the TAKS-math scores was 75 percent passing. A parent in Tyler, TX...

The state average for the TAKS-math scores was 75 percent passing. A parent in Tyler, TX claims that students are doing much worse than the state passing rate. The high-school principal in Tyler, TX, summarized her latest TAKS-math scores from the 11th grade. Out of 120 students, 85 got a passing TAKS-math score. Is there evidence at the 5% level to support the parent’s claim? What are the null and alternative hypotheses for this test? a) Ho: p ≥≥ 0.75...

GRE math scores are normally distributed with a mean µ = 500 and standard deviation, ...

GRE math scores are normally distributed with a mean µ = 500 and standard deviation,  = 55. This year Howard University admitted 1500 graduate students. Calculate: a. the number of students with test scores above 520, below 490, between 482 & 522 b. how high a score is needed to be in the top 10%, top 5%?

1. SAT math scores are normally distributed with a mean 525 and a standard deviation of...

1. SAT math scores are normally distributed with a mean 525 and a standard deviation of 102. In order to qualify for a college you are interested in attending your SAT math score must be in the highest 9.34% of all SAT scores. What is the minimum score you need on the SAT to qualify for the college? 2. If you get into this college you are interested in running for the track team. To qualify for the track team...

Math SAT scores are known to be normally distributed with mean of 500 and standard deviation...

Math SAT scores are known to be normally distributed with mean of 500 and standard deviation of 100. Answer the following questions. (I also want to see good notation and some of your calculations.) a) Suppose we randomly select one person who has taken the SAT. What is the probability their math score is between 525 and 550? b) Suppose we randomly select 25 people who have taken the SAT. What is the probability their average math score is between...

Math SAT scores (Y) are normally distributed with a mean of 1500 and a standard deviation...

Math SAT scores (Y) are normally distributed with a mean of 1500 and a standard deviation of 140. An evening school advertises that it can improve students' scores by roughly a third of a standard deviation, or 30 points, if they attend a course which runs over several weeks. (A similar claim is made for attending a verbal SAT course.) The statistician for a consumer protection agency suspects that the courses are not effective. She views the situation as follows:...

The following data is the math test scores of students graduating from a particular high school....

The following data is the math test scores of students graduating from a particular high school. The government uses these scores to determine if there will be accreditation awarded. In order for this to occur the mean score must be above 780. A sample of students' scores is drawn at random and they take the test. The scores are in the following table and the population is considered a normal distribution. Test at the .01 level. 980 764 798 760...