### Statistical Analysis of Procrastination Among College Students#### Claim and HypothesisOne study reported that **86%** of college students identify themselves as procrastinators. A professor challenges this claim, suspecting that the percentage might be lower. To test this hypothesis, the professor conducts a simple random sample consisting of **139 college students**, finding that **110** of them identify as procrastinators.#### ObjectiveDetermine whether the professor's sample supports the hypothesis that fewer than **86%** of college students are procrastinators, utilizing a **0.05 level of significance**.#### Steps to Conduct the Hypothesis Test:**Step 3 of 3: Draw a conclusion and interpret the decision.**This step involves concluding if the sample evidence provides sufficient basis to reject the initial claim.#### Conclusion Drawing and Interpretation:1. **Estimate Population Proportion**: Calculate the sample proportion (p̂) of procrastinators: \[ \hat{p} = \frac{110}{139} \approx 0.791 \]2. **Formulate Hypotheses**: - Null Hypothesis (H₀): \( p \geq 0.86 \) - Alternative Hypothesis (H₁): \( p < 0.86 \)3. **Calculate Test Statistic**: Apply the z-test for proportion: \[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}} = \frac{0.791 - 0.86}{\sqrt{\frac{0.86 \cdot (1 - 0.86)}{139}}} \]4. **Determine Critical Value and p-value**: - Critical value for a one-tailed test at 0.05 significance: \( z_{0.05} \approx -1.645 \) - Compare calculated z-value with this critical value or calculate the p-value for z.5. **Make a Decision**: - If z calculated > critical z, fail to reject H₀. - If z calculated < critical z, reject H₀.6. **Interpret the Decision**: - Based on the above comparison, derive whether the evidence strongly counters or supports the professor's claim. A decision to reject H₀ would indicate evidence supporting that fewer

The question is about hypo. testingGiven :Popl. prop. of college stud. identify themselves as…

Answered: One study claimed that 86 % of college…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 315 people over the age of 55, 61 dream in black and white, and among 285 people under the age of 25, 12 dream in black and white. Use a 0.01 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts (a) through (c) below. a. Test the claim using a hypothesis test. Consider the first sample to be the sample of people over the age of 55 and the second sample to be the sample of people under the age of 25. What are the null and alternative hypotheses for the hypothesis test? O A. Ho: P1 = P2 H1: P1 > P2 O B. Ho: P1 # P2 H1: P1 = P2 OC. Ho: P1 = P2 H;:Pq
The Bureau of Labor Statistics reports that the official unemployment rate for Black people was 10.4% and 4.7% for White people in February 2015. Select all correct answers for this question. O The samples of white and black people are independent. The explanatory variable is the unemployment rate. The response variable is the unemployment rate. The response variable is race.
Magazine A national publishing house claims that 28% of all weekly magazine readers in SA read their publication. Test this claim at the 1% significance level, if a survey found that 104 out of a random sample of 400 magazine readers said that they read the specific publication.
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Recent research commissioned by Vodafone suggests that older workers are the happiest employees (BBC News, July 21, 2008). The report documents that 70% of older workers in England feel fulfilled, compared with just 50% of younger workers. A demographer believes that an identical pattern does not exist in Asia. A survey of 120 older workers in Asia finds that 78 feel fulfilled. At a 5% level of significance, test if older workers in Asia feel less fulfilled than their British counterparts. In the box below, answer the following (a) What is the p-value for the test? (Round to three decimal places.) (b) At a 5% level of significance, do older workers in Asia feel less fulfilled than their British counterparts?
Because the confidence interval limits v 0, it appears that the two proportions are V Because the confidence interval limits include V values, it appears that the proportion of people over 55 who dream in black and white is V the proportion for those under 25. c. An explanation for the results is that those over the age of 55 grew up exposed to media that was displayed in black and white. Can these results be used to verify that explanation? O A. No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white, but the results cannot be used to verify the cause of such a difference. O B. No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white, but the results are not statistically significant enough to verify the cause of such a difference. O C. Yes. The results can be used to verify the given explanation because difference in proportions is…
A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 303 people over the age of 55, 79 dream in black and white, and among 300 people under the age of 25, 18 dream in black and white. Use a 0.01 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts (a) through (c) below. a. Test the claim using a hypothesis test. Consider the first sample to be the sample of people over the age of 55 and the second sample to be the sample of people under the age of 25. What are the null and alternative hypotheses for the hypothesis test? O A. Ho: P₁ = P₂ H₁: P₁ P2 O D. Ho: P₁ #P₂ H₁: P₁ = P2 Identify the test statistic. z=0 Z= (Round to two decimal places as needed.) Identify the P-value. P-value= (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? the significance level of a = 0.01, so…
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A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 323 people over the age of 55, 71 dream in black and white, and among 288 people under the age of 25, 14 dream in black and white. Use a 0.05 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts (a) through (c) below. Question content area bottom Part 1 a. Test the claim using a hypothesis test. Consider the first sample to be the sample of people over the age of 55 and the second sample to be the sample of people under the age of 25. What are the null and alternative hypotheses for the hypothesis test? A. H0: p1=p2 H1: p1<p2 B. H0: p1≥p2 H1: p1≠p2 C. H0: p1≠p2 H1: p1=p2 D. H0: p1≤p2 H1: p1≠p2 E. H0: p1=p2 H1: p1>p2 Your answer is correct. F. H0: p1=p2 H1:…
In a poll conducted by The New York Times and CBS News, 44% of Americans approve of the job that the Supreme Court is doing (The New York Times, June 8, 2012). Assume that this percentage was true for the population of Americans at the time of this poll was conducted. A recent poll of 1265 Americans showed that 38% of them approve of the job that the Supreme Court is doing. At a 2% significance level, can you conclude that the current proportion of Americans who approve of the job that the Supreme Court is doing is different from 44%?Round your answers to two decimal places.zobserved =zcritical left =zcritical right =We (reject, fail to reject) the null hypothesis. We conclude that the current proportion of Americans who approve of the job that the Supreme Court is doing is Choose your answer; We conclude that the current proportion of Americans who approve of the job that the Supreme Court is doing is (not different from, different…
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