A decade-old study found that the proportion of high school seniors who felt that "getting rich" was an important personal goal was 65%. Suppose that we have reason to believe that this proportion has changed, and we wish to carry out a hypothesis test to see if our belief can be supported. State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_a \) that we would use for this test.**Hypotheses:**\[ H_0: \,\, p = 0.65 \]\[ H_a: \,\, p \neq 0.65 \]The image includes a box for writing hypotheses and a set of symbols and templates to help construct the null and alternative hypotheses. The provided elements include symbols for mean (\(\mu\)), proportion (\(p\)), standard deviation (\(\sigma\)), and others, alongside various mathematical and statistical operations.

Given thatA decade-old study found that the proportion of high school seniors who felt that "Getting…

Answered: A decade-old study found that the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Please answer question 10.5
Question #1
• Question 16 A news article that you read stated that 53% of voters prefer the Democratic candidate. You think that the actual percent is different. 122 of the 272 voters that you surveyed said that they prefer the Democratic candidate. What can be concluded at the 0.10 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: ?v| Select an answerv (please enter a decimal) H1: |?vSeect an answerV (Please enter a decimal) c. The test statistic ?v = (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is ?v a f. Based on this, we should Select an answerv the null hypothesis. g. Thus, the final conclusion is that ... O The data suggest the population proportion is not significantly different 53% at a = 0.10, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different 53%. O The data…
Example 2: A meteorologist was interested in determining whether or not there was higher average rainfall during certain seasons of the year in her local community. She randomly sampled 7 days from each season and recorded the amount of rainfall in her local community on that day. Carry out an appropriate hypothesis test at the a = 0.02 level to determine if there is evidence that the true average rainfall is higher in some seasons than others. The data is shown below where the rainfall is measured in inches. %3D
Question 5 (10 marks) a. Write the null and alternative hypothesis for the following and determine if it is a two-tailed, a left-tailed or a right-tailed test. i. A researcher is studying the effects of radical exercise program on knee surgery patients. There is a good chance the therapy will improve recovery time, but there's also the possibility it will make it worse. Average recovery times for knee surgery patients is 8.2 weeks. ii. Alumni group of a private institution wants to test if the college student, on the average, take less than 4 years to graduate.
Question 29 If the p-value is less than alpha in a one-tail test, what decision can you make? O A two-tail test should be used. O The null hypothesis should not be rejected. O Alpha should be changed. O The null hypothesis should be rejected.
A random sample of n = 25 is obtained from a population with variance ?2, and the sample mean is computed to be ?̅= 70. Consider the null hypothesis ?0: ? =80 versus the alternative hypothesis ?1: ? < 80. Compute the p-value when the population variance is ?2 = 600.
QUESTION 2 You conduct a study to understand whether happy people are more likely to exercise than sad people. In your sample of happy people. 25 chose to exercise and 10 chose to take a nap. In your sample of sad people, 5 chose to exercise and 35 chose to take a nap. (1) What is the null hypothesis? a. There is a difference in rates of exercise among happy and sad people. b. There is an association in rates of exercise among happy and sad people. c. There is not a difference in rates of exercise among happy and sad people. d. There is not an association in rates of happiness among those who exercise and those who nap. (2) What is the expected frequency for happy people who exercise? (3) What is the expected frequency for sad people who exercise? (4) What is the expected frequency for happy people who nap? (5) What is the expected frequency for sad people who nap? (6) What is your chi-square value? (7) How many degrees of freedom are there? (8) Assuming alpha is equal to .05, what is…
Answer A, B1, and B2: A. 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. B. Researchers interested in lead exposure due to car exhaust sampled the blood of 52 police officers subjected to constant inhalation of automobile exhaust fumes while working traffic enforcement in a primarily urban environment. The blood samples of these officers had an average lead concentration of 124.32 µg/l and a SD of 37.74 µg/l; a previous study of individuals from a nearby suburb, with no history of exposure, found an average blood level…
According to a University Center for Logistics Management, 18% of all merchandise sold in the United States gets returned. A San Francisco department store sampled 100 items sold in January and found that 19 of the items were returned.If you have the following null and alternative hypotheses for a test you are running:H0:p=0.18Ha:p≠0.18Calculate the test statistic, rounded to 3 decimal places
What is the value of the sample test statistic? (Test the difference p₁ - P2. Do not use rounded values. Round your final answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. 0-3 -2 -2 -1 -1 0 Read It 0 1 1 Watch it 2 2 3 0-3 ^ -1 0 1 -2 -2 -1 0 1 O At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. 2 2 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. O At the a= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. 3…
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