Question

In: Statistics and Probability

Score on a 100-point test is normally distributed with mean 87.7.   You took a sample of...

  1. Score on a 100-point test is normally distributed with mean 87.7.   You took a sample of 36 students. The mean for this group is 92 and the standard deviation is 15.              
    1. Test the hypothesis that the performance of this group is different than the regular student population. Use α=.05.
  • What is the alternative hypothesis?
  • What is the value of the test statistic?
  • would you use the t test?
  • What is the rejection region?
  • the decision is to not reject the null hypothesis. Yes or No?
    1. Test the hypothesis that the performance of this group is better than the regular student population, i.e., their score is greater than the normal population. Use α=.05
  • What is the alternative hypothesis?
  • What is the rejection region?
  • the decision is to not reject the null hypothesis. Yes or No?
  • the 95% confidence interval for the population mean is?
  1. Score on a 20-point assignment is normally distributed with a mean of 15 and standard deviation of 5. You believe that your friends are smarter and that their average is greater. You took a sample of 9 of your friends. The mean for this group is 18.  
  • What is the rejection region?
  • Would you use the t test?
  • The 95% confidence interval for the population mean is

Solutions

Expert Solution


Related Solutions

Score (X) on a 100-point test is normally distributed with mean 89 and standard deviation 10.                           
Score (X) on a 100-point test is normally distributed with mean 89 and standard deviation 10.                                                          What is the following probability: P(85 < X < 95) You took a sample of 25 students from the population in I. What is the following probability:                P(85 < Xbar < 95)
Stanford–Binet IQ Test scores are normally distributed with a mean score of 100 and a standard...
Stanford–Binet IQ Test scores are normally distributed with a mean score of 100 and a standard deviation of 18. (b) Write the equation that gives the z score corresponding to a Stanford–Binet IQ test score. z = (x – 100 ) / 18 (c) Find the probability that a randomly selected person has an IQ test score. (Round your answers to 4 decimal places.) 1. P(x > 135) 2. P(x < 89) 3. P(71 < x < 129) − =...
Stanford–Binet IQ Test scores are normally distributed with a mean score of 100 and a standard...
Stanford–Binet IQ Test scores are normally distributed with a mean score of 100 and a standard deviation of 18. (b) Write the equation that gives the z score corresponding to a Stanford–Binet IQ test score. z = (x – 100 ) / 18 (c) Find the probability that a randomly selected person has an IQ test score. (Round your answers to 4 decimal places.) 1. P(x > 135) 2. P(x < 89) 3. P(71 < x < 129) − =...
Stanford–Binet IQ Test scores are normally distributed with a mean score of 100 and a standard...
Stanford–Binet IQ Test scores are normally distributed with a mean score of 100 and a standard deviation of 11. (b) Write the equation that gives the z score corresponding to a Stanford–Binet IQ test score. z = (x – 100 ) / 11 (c) Find the probability that a randomly selected person has an IQ test score. (Round your answers to 4 decimal places.) 1. P(x > 134) .001 2. P(x < 80) .0345 3. P(84 < x < 116)...
An instructor gives a 100-point test in which the grades are approximately normally distributed. The mean...
An instructor gives a 100-point test in which the grades are approximately normally distributed. The mean is 65 points and the standard deviation is 12 points. a. What is the lowest possible score to qualify in the top 5% of the scores? b. If 500 students took the test, how many students received a score between 60 and 80 points? ( I hope the solution to the questions can be provided as well )
The score for a special personality test are normally distributed with a mean of 60 and...
The score for a special personality test are normally distributed with a mean of 60 and standard deviation of 6. a) What is the probability that one person who took the test, chosen at random, will have scored less than 65? b) Random samples of 16 people who took the test are surveyed. What is the probability that the mean of these samples is less than 65?
IQ scores are known to be normally distributed. The mean IQ score is 100 and the...
IQ scores are known to be normally distributed. The mean IQ score is 100 and the standard deviation is 15. What percent of the population has an IQ between 85 and 105. Need to solve it through Excel
A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was...
A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was 21.4 and the standard deviation was 5.4. The test scores of four students selected at random are 15​, 22​, 9​, and 36. Find the​ z-scores that correspond to each value and determine whether any of the values are unusual. The z-score for 15 is:
A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was...
A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was 1507 and the standard deviation was 315. The test scores of four students selected at random are 1900​, 1260​, 2220​, and 1390. Find the​ z-scores that correspond to each value and determine whether any of the values are unusual. The​ z-score for 1900 is nothing. ​(Round to two decimal places as​ needed.) The​ z-score for 1260 is nothing. ​(Round to two decimal places as​...
A sample of test scores is normally distributed with a mean equal to 22 and a...
A sample of test scores is normally distributed with a mean equal to 22 and a variance equal to 25. Part (a) What percentage of scores are between 17 and 27? (Round your answer to two decimal places.) ____% Part (b) What raw score is the cutoff for the top 10% of scores? (Round your answer to one decimal place.) Part (c) What is the proportion below 15? (Round your answer to four decimal places.) Part (d) What is the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT