Exercise 3 - Hypotheses You observe that a server attack occurs more rarely on weekends. To test that statistically: a) Formulate an appropriate working hypothesis. b) Formulate the null hypothesis. c) How can you falsify the hypothesis? ,
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- In a hypothesis test, the null hypothesis states that the population proportion of individuals who support a certain political candidate is equal to 0.6. A sample of size 400 is taken and 175 individuals support the candidate. What is the Z-score for this hypothesis test?You may need to use the appropriate appendix table or technology to answer this question. Carl Allen and Norm Nixon are two loan officers at a certain bank. The bank manager is interested in comparing the default rate on the loans approved by Carl to the default rate on the loans approved by Norm. In the sample of loans collected, there are 70 loans approved by Carl (14 of which defaulted) and 80 loans approved by Norm (9 of which defaulted). (a) State the hypothesis test that the default rates are the same for the two loan officers. (Let p1 = the population proportion of Carl's loans that default, and let p2 = the population proportion of Norm's loans that default. Enter != for ≠ as needed.) H0: Ha: (b) What is the sample default proportion for Carl? What is the sample default proportion for Norm? (c) Use a 0.05 level of significance. Calculate the test statistic. (Use p1 − p2. Round your answer to two decimal places.) What is the p-value? (Round…Q4
- Does college major depend on gender? Researchers ask a group of college students about their majors. They also group the students by their gender. The data are recorded in the contingency table below, and a chi-square Test of Independence at the 5% significance level is performed. Arts Humanities Sciences Row Total Men 11 5 19 35 Women 11 22 9 42 Column Total 22 27 28 77 (a) The null and alternative hypotheses are: H0: The two variables are independent, so gender does not affect college major. Ha: The two variables are dependent, so gender does affect college major. (b) Compute the test statistic, rounded to one decimal place. (Use expected frequencies that are also rounded to one decimal place.)PART B (b) Based on your answer to part (a), which of the following statements is true? ____ Since the p- valueis less than the significance level, the null hypothesis is rejected. _____ Since the p- valueis less than the significance level, the null hypothesis is not rejected. ____ Since the p- valueis greater than the significance level, the null hypothesis is rejected. ___ Since the p- valueis greater than the significance level, the null hypothesis is not rejected.1. (Hypothesis Testing) Dr. Ayati claims that 90% of her students are satisfied with the data science course. Jose was not very satisfied, and he suspected the student evaluation is false. He surveyed a random sample of 80 of Dr. Ayati's students and found that only 80% were satisfied. He also run 1000 simulation, each simulating a sample of 80 students assuming there are 90% satisfied students. % of satisfied students Frequency 80 5 82.5 24 85 72 87.5 181 90 281 92.5 272 95 136 97.5 27 100 2 (a) What is the null hypothesis and alternative hypothesis Jose is testing? (b) According to the simulation, what is the probability of getting a sample with 80% satisfied students or less? (c) What should Jose conclude regarding the hypothesis?
- You may need to use the appropriate appendix table or technology to answer this question. Carl Allen and Norm Nixon are two loan officers at a certain bank. The bank manager is interested in comparing the default rate on the loans approved by Carl to the default rate on the loans approved by Norm. In the sample of loans collected, there are 70 loans approved by Carl (21 of which defaulted) and 80 loans approved by Norm (17 of which defaulted). (a) State the hypothesis test that the default rates are the same for the two loan officers. (Let p1 = the population proportion of Carl's loans that default, and let p2 = the population proportion of Norm's loans that default. Enter != for ≠ as needed.) H0: Ha: (b) What is the sample default proportion for Carl? What is the sample default proportion for Norm? (c) Use a 0.05 level of significance. Calculate the test statistic. (Use p1 − p2. Round your answer to two decimal places.) What is the p-value? (Round…1. If x- = 16, then x A. 16 В. -16 1 C. 16 D. None of the other choicesDreamfilms Studios boasts that its summer features are so good that at least half of all tickets sold one summer are for its films. A competing studio claims that less than half of all tickets sold are for Dreamfilms' movies. After the hypothesis test is completed, the conclusion is to fail to reject the null hypothesis. If the true percentage of tickets sold for Dreamfilms Studios' movies that summer was only 48%, was an error committed? If so, what type?
- You watch people exiting Dodgers stadium after a game and you write down the number of males and the number of females that exit the stadium past you during the 20 minutes that you spend watching. You assumed that there would be a perfectly equal number of males and females attending a Dodgers game, but you look at the number of males and females that you actually counted, and you see if you still think that is actually true. What kind of hypothesis test would allow you to do this? a. One-Factor, Independent-Measures ANOVA b. Two-Factor ANOVA c. Correlation/Regression d. Chi-Square Goodness of FitUSE THE 8-STEP HYPOTHESIS TESTING Refer to the study by Carter et al. [A-9], who investigated the effect of age at onset of bipolar disorder on the course of the illness. One of the variables studied was subjects' family history. Table 3.4.1 shows the frequency of a family history of mood disorders in the two groups of interest: early age at onset (18 years or younger) and later age at onset (later than 18 years). Family History of Mood Disorders Early ≤ 18(E) 28 19 41 53 Later > 18 (L) 35 38 44 60 141 Total 63 57 85 113 Negative (A) Bipolar disorder (B) Unipolar (C) Unipolar and bipolar (D) Total 177 318 Source: Tasha D. Carter, Emanuela Mundo, Sagar V. Parkh, and James L. Kennedy, "Early Age at Onset as a Risk Factor for Poor Outcome of Bipolar Disorder," Journal of Psychiatric Research, 37 (2003), 297-303. Can we conclude on the basis of these data that subjects 18 or younger differ from subjects older than 18 with respect to family histories of mood disorders? Let a = .05.(b) A t-test has two possible outcomes: reject or do not reject the null hypothesis. Suppose the null hypothesis is true. If the null hypothesis is rejected, the result is statistically significant, which would be a Type I error; if the null hypothesis is not rejected, the result is not statistically significant, which would not be a Type I error. Let S represent a statistically significant result, and let Nrepresent a result that is not statistically significant. (i) If P(S)=0.05, what is the value of P(N) ?