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 u = 521. The teacher obtains a random sample of 2200 students, puts them through the review class, and finds that the mean math score of the 2200 students is 526 with a standard deviation of 119. Complete parts (a) through (d) below. (a) State the null and alternative hypotheses. Let u be the mean score. Choose the correct answer below. O A. Ho: u> 521, H,: u#521 O B. Ho: H= 521, H,: u# 521 C. Họ: H= 521, H,: u > 521 O D. Ho: H< 521, H,: u> 521 (b) Test the hypothesis at the a = 0.10 level of significance. Is a mean math score of 526 statistically significantly higher than 521? Conduct a hypothesis test using the P-value approach. Find the test statistic. to = (Round to two decimal places as needed.)

Assume that adults have iq scores that are normally distributed with a mean of 98.2 and a standard deviation 17. Find the first quartile Q1, which is the IQ score separating the bottom 25% from the top 75%. The first quartile is

The time it needs a communications worker to arrange a domestic phone call is normally distributed with mean  Fifty seconds and a standard deviation of  Eight seconds. Find the proportion of times that someone has to wait for more than a minute for the call to be placed.

Each students in a local school district write a national examination. The average on this year national exam is 150 with a standard deviation of 20. Schools where the overall average is between 1.5 and 3.0 standard deviations above the mean are eligible for additional funding. What is the average range a school must achieve to be eligible for funding?

The length of songs in the Big Hair playlist of a Statistics professor's mp3 player varies from song to song. This variation can be modeled by the normal distribution, with a mean song length of �=4.3 minutes and a standard deviation of �=0.65 minutes. (Note that a song that has a length of 4.5 minutes is a song that lasts for 4 minutes and 30 seconds.)The professor decides to shuffle the playlist, which means that the mp3 player will randomly pick a song within this particular playlist and play it next.(a) What is the probability that the next song to be played is between 3.9 and 4.85 minutes long? Answer to four decimals. (b) What proportion of all the songs in this playlist are longer than 5 minutes? Use four decimals in your answer. (c) 20% of all the songs in this playlist are at most how long, in minutes? Enter your answer to two decimals. minutes(d) There are 247 songs in the Big Hair playlist. How many of these would you expect to be longer than 5 minutes in length? Use two…

A Statistics instructor wanted to compare the scores on the same final exam given to students at a local community college and local university.  The Statistics instructor feels that students at the community college would be better prepared and have higher exam scores on the final exam. After grading the final exams from both institutions, the Statistics instructor found that for a sample of 36 community college students, the sample had a mean score of 84 with a standard deviation of 3.4.  A sample of 45 university students had a mean score 79 with a standard deviation of 2.6.  Construct a 95% confidence interval for the difference between population mean exam scores. Round your final results to one decimal place.      _____________     ≤      ???  −  ?????      ≤     ______________

Jason's z- score in the 10-k run was -3. if the raw score standard deviation was 5, and the mean running time for the competitors was 55 minutes, what was Jason's raw score running time?

A radio station claims that the amount of advertising each hour has a mean of 17 minutes and a standard deviation of 1.7 minutes. You listen to the radio station for 1 hour and observe that the amount of advertising time is 7 minutes. Calculate the z-score for this amount of advertising time.

A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was 1549 and the standard deviation was 318. The test scores of four students selected at random are 1960​,1270​, 2250​, and 1450. Find the​ z-scores that correspond to each value and determine whether any of the values are unusual.

A community college Math instructor feels that the average age of community college students decreased since they started teaching 25 years ago.  Looking up data from the year the instructor started teaching, the mean age of community college students was 24.3 years old, with a population standard deviation of 2.2 years.  The Math instructor took a sample of 40 of their current community college students and found that the sample had a mean age of 23.7 years old.  Assume the population of ages of community college students is normally distributed and that the population standard deviation has remained the same. Test at the 5% significance level if the mean age of community college students is now less than 24.3 years old. Choose the correct answer from the parenthesis. (i)  Hypotheses       ?0:   ?  =  ( 0, 2.2, 22.7, 24.3, 25, 40) ______________ .     ?1:    ?  =  ( < , > ) ______________   ( 0, 2.2, 22.7, 24.3, 25, 40) ________________ . (ii)  Test Statistic     ( z/ t )…