In the past, 60% of all undergraduate students enrolled at a State University in NY earned their degrees within four years of matriculation. Administrators want to test the claim made by some faculty memebers that this proportion has fallen below the historical value of 60%. A random sample of 95 students from the class that matriculated in the fall of 2012 was recently selected to test this hypothesis. Administrators found that 44 of these 95 students graduated in the spring of 2016 (i.e., four academic years after matriculation). Use a significance level of 5%. a) Formulate the hypotheses. b) What is the value of the test statistic? c) What is the critical value of the test?

In the past, 60% of all undergraduate students enrolled at a State University in NY earned their degrees within four years of matriculation. Administrators want to test the claim made by some faculty memebers that this proportion has fallen below the historical value of 60%. A random sample of 95 students from the class that matriculated in the fall of 2012 was recently selected to test this hypothesis. Administrators found that 44 of these 95 students graduated in the spring of 2016 (i.e., four academic years after matriculation). Use a significance level of 5%. a) Formulate the hypotheses. b) What is the value of the test statistic? c) What is the critical value of the test?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

The National Academy of Science reported that 33% of research in mathematics is published by US authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 33%. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 280 recent articles published by reputable mathematics research journals and finds that 108 of these articles have US authors. Does this evidence support the mathematics chairperson’s claim that the percentage is no longer 33%? Use a 0.01 level of significance. Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below. H0: p = 0.33 Ha: p___ 0.33
In a previous poll, 35% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose that, in a more recent poll, 1088 adults with children under the age of 18 were selected at random, and 361 of those 1088 adults reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the a = 0.05 significance level. are satisfied. (Round to one decimal place as needed.) What are the null and alternative hypotheses? 0.35 versus H,: p < 0.35 Ho: p (Type integers or decimals. Do not round.) Find the test statistic, zo- Z, = - 1.26 (Round to two decimal places as needed.) Find the P-value. P-value = (Round to three decimal places as needed.) Enter your answer in the answer box and then click Check Answer. Check Answer 1 Clear All 1 part remainina
In 2016, the New York Times reported that the average American spent 50 minutes per day on Facebook, as compared to an average of 42 minutes per day reading, exercising, or actually socializing combined. You suspect that this gap has widened over the years, and collect a random sample of 100 people. For 50 of them (again, randomly chosen from your sample), you track their time spent on Facebook; you track the other 50 peoples’ total time spent reading/exercising/socializing. (a) Say the 2016 figures regarding Americans’ time allotments still hold true. If the population standard deviation for minutes using Facebook is 12.5 minutes, and the population standard deviation for minutes spent on reading, exercising, and socializing (referred to from here on as ”Other” activities) is 8 minutes, what are the expected value and the standard error of the difference between the average amount of time spent on Facebook and the average amount of time spent on Other activities computed from a sample…
The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population. a. Is this a test of one mean or proportion? b. State the null and alternative hypotheses. HO: c. Is this a right-tailed, left-tailed, or two-tailed test? d. What symbol represents the random variable for this test? e. In words, define the random variable for this test. f. Calculate the following: i. x = ii. n=. lii. p' = g. Calculate ox = h. State the distribution to use for the hypothesis test. i. Find the p-value. j. At a pre-conceived a = 0.05, what is your: i. Decision: ii.…
A nonprofit company concerned with the school dropout rates has designed a tutoring program aimed at students between 16 to 18 years old. A national center for educational statistics reported that the high school dropout rate for the year 2000 was 10.9%.One school district, who adopted the use of the nonprofit's tutoring program and whose dropout rate has always been very close to the national average, reported in 2004 that 158 of their 1769 students dropped out. Is their experience evidence that the tutoring program has been effective? Determine the hypotheses for this test. Choose the correct answer below A. H0: p=0.109 HA: p≠0.109 B. H0: p≠0.109 HA: p=0.109 C. H0: p=0.109 HA: p<0.109 D. H0: p=0.109 HA: p≥0.109 E. H0: p≥0.109 HA: p=0.109 F. H0: p≤0.109 HA: p=0.109 Compute the test statistic. enter your response here *______* Find the P-value. enter your response here* ______* 3. Is their experience evidence that the tutoring…
The National Academy of Science reported that 41% of research in mathematics is published by US authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 41%. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 186 recent articles published by reputable mathematics research journals and finds that 92 of these articles have US authors. Does this evidence support the mathematics chairperson’s claim that the percentage is no longer 41%? Use a 0.05 level of significance. Step 1 of 3: State the null and alternative hypotheses for the test. circle the answer below. H0 p=0.41 ha: p⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯0.41 A.<B.≠C.> Step 2 of 3: Compute the value of the test statistic. Round your answer to two decimal places Step 3 of 3: Draw a conclusion and interpret the decision. A. We reject the null hypothesis and conclude that there is insufficient evidence at a…
1. The percentage of 12- to 17-year-olds who reported talking at least once in the past year with their parents about the dangers of drug, tobacco, or alcohol is 60% nationally. A state youth council believes this proportion is higher in their state, where there has been an intense media campaign about this issue. A survey of randomly chosen students from across the state shows 1032 of 1642 students reporting they are having these conversations with their parents. Is there evidence that the percent of students using drugs, tobacco or alcohol in this state is above the national rate?
The National Academy of Science reported that 33 % of research in mathematics is published by US authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 33 %. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 280 recent articles published by reputable mathematics research journals and finds that 108 of these articles have US authors. Does this evidence support the mathematics chairperson's claim that the percentage is no longer 33 % ? Use a 0.01 level of significance. Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below. Answer Ho :p = 0.33 Ha P O # ο ο ο HAV O < 0.33 Tables Keypad Keyboard Shortcuts
In a previous poll, 38% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose that, in a more recent poll, 1186 adults with children under the age of 18 were selected at random, and 428 of those 1186 adults reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the α = 0.01 significance level. Because npo (1-Po) = 279.4 > 10 and the sample size is (Round to one decimal place as needed.) What are the null and alternative hypotheses? но: р = 0.38 versus H₁: p (Type integers or decimals. Do not round.) Find the test statistic, Zo. < 0.38 Zo -1.36 (Round to two decimal places as needed.) = Find the P-value. P-value = (Round to three decimal places as needed.) less than 5% of the population size, and the adults in the sample were selected at random, all of…
In a current study, a random sample of 20 teachers from Georgia and an independent random sample of 20 teachers from Indiana have been asked to report their annual income. The data obtained are as follows. Georgia 33567, 41744, 51186, 30464, 51606, 42617, 48830, 41455, 49371, 40828, 44007, 42605, 34923, 30519, 42581, 52952, 45651, 45084, 35455, 27800 Send data to calculator Indiana Annual income in dollars 29227, 35464, 45458, 32113, 29125, 38494, 23709, 32874, 34046, 21221, 39527, 56140, 38977, 47806, 44866, 36325, 34654, 38647, 37073, 36344 Send data to Excel The population standard deviations for the annual incomes of teachers in Georgia and in Indiana are estimated as $6500 and $6350, respectively. It is also known that both populations are approximately normally distributed. Construct a 90% confidence interval for the difference between the mean annual income of teachers from Georgia (,) and the mean annual income of teachers from Indiana (₂). Then find the lower limit and upper…
Based on information from Harper's Index, 37 out of a random sample of 100 adult Americans who did not attend college believe in extraterrestrials. However, out of a random sample of 100 adult Americans who did attend college, 47 claim that they believe in extraterrestrials. Does this indicate that the proportion of people who attend college and who believe in extraterrestrials is higher than the proportion who did not attend college? (a) State the hypotheses in plain language. (b) Fill in the table below, then enter this table in the left side of the Rossman-Chance applet. No college College Total Believe in ETs 84 Did not believe in ETs 116 Total 100 100 200 (c) Compute the point estimate for the difference in the proportion believing in extraterrestrials between those not attending college and those attending college. Pne – Pe = (d) Complete at least 1000 simulations in the Rossman-Chance app 2 and report your findings below. (For help with the applet, refer to the e "Using the…
Express House Delivery Service provides high quality service to customers. The company guarantees a refund of all charges if a package it is delivering does not arrive at its destination by the specified time. It is known from past data that despite all efforts, 2% of the packages mailed through this company do not arrive at their destinations within the specified time. Suppose a corporation mails 10 packages through Express House Delivery Service on a certain day.