stats13_hw4

.pdf

School

University of California, Los Angeles *

*We aren’t endorsed by this school

Course

Subject

Statistics

Date

May 10, 2024

Type

pdf

Pages

Uploaded by SuperNeutron3121 on coursehero.com

Akansha Magal 005697881 Dis 1B Stats 13 Homework 4 Question 1 2.1.37 a. Null hypothesis: There is no evidence that less than one-fourth of the sharks in the aquarium are diseased. Alternative hypothesis: There is evidence that less than one-fourth of the sharks in the aquarium are diseased. b. The value of the statistic is 3/15, or 0.20. Question 2 2.1.38 a. The p-value for the hypotheses in the previous question I found was 0.4460. b. The simulation-based p-value is 0.4460, so assuming the null hypothesis, then there is a 44.60% chance that in a random sample of 15 sharks that less than one-fourth of the sharks are diseased. Since the p-value is much greater than 0.10, there is not much evidence in support of the alternative hypothesis that there is evidence that less than one-fourth of the sharks in the aquarium are diseased. c. I am comfortable drawing my conclusion about the 243 sharks living in the large aquarium at the zoo because my sample is a subset of the shark population not at the zoo. I cannot, for example, generalize my information from my sample to the population of all sharks since my sample of sharks at the aquarium might not even be representative of the population of sharks at the zoo, let alone all sharks. d. A theory-based approach would not be reasonable for these data because 3 successes (sharks that have the disease) and 12 failures (sharks that do not have the disease) does not fulfill the validity condition that says you should have at least 10 successes and

10 failures in your sample to be fairly confident that a normal distribution will fit the simulated null distribution nicely. Question 3 2.2.2 (3500+4000+4500)/3=4000 (3600+4100+4600)/3=4100 B. The average would increase. Question 4 2.2.3 A. The standard deviation would stay the same. Question 5 2.2.7 a. The observational units would be the students in the instructor’s class. b. The variable recorded is how many states the students have visited in the US. This is a quantitative variable. c. The shape of the distribution is not very symmetric. Most of the data is clustered towards the left of the dot plot, corresponding to fewer states visited in the US. A typical number of states visited is between 1 and 15 states; the data is centered around 6 or 7 states. Because most of the data is within this certain set of values, there is generally low variability in the data. Most students in the instructor’s class have not traveled the US that much and have visited only a few states. d. 1, 1, 3, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 12, 12, 12, 12, 13, 14, 15, 15, 15, 16, 25, 30, 43 The median value for the number of states visited by the students in this study is (7+8)/2 or 7.5 states. e. The mean value for these data would be larger than the median. This is because the data is right-skewed, meaning the balance is shifted to the right by a few very large values. f. Mean: Smaller Median: Same Standard deviation: Smaller Question 6 2.2.12 a. The number 3.01 is a statistic. b. I would assign the symbol x̄ to the number 3.01. c. Using the Theory-Based Inference applet, I would select the scenario as “One mean” and check the box for the “Test of significance” option. I would fill in μ=2.75 to represent the null hypothesis that the average number of hours per day Cal Poly students spend watching TV is 2.75 hours, and I would fill in μ ≠ 2.75 to represent the two-sided alternative hypothesis that the average number of

hours per day Cal Poly students spend watching TV is different from 2.75 hours. I would fill in the given information that n=100 since Dr. Sameer is surveying a sample of100 Cal Poly students, the observed statistic x̄ = 3.01, and the sample standard deviation s. To find the p-value, I would then analyze the null distribution for the proportion of the simulated statistics that are at least as extreme as 3.01 in either direction since the alternative hypothesis is two-sided. The smaller the proportion of statistics at least as extreme as 3.01, the stronger the evidence is against the null hypothesis because it becomes less likely that the average number of hours per day Cal Poly students spend watching TV is 2.75 hours. d. One repetition= one set of 100 Cal Poly students surveyed by Dr. Sameer Null model= The average number of hours per day Cal Poly students spend watching TV is 2.75 hours. Statistic= 3.01 hours per day spent watching TV Question 7 2.2.13 a. If the average number of hours per day Cal Poly students spend watching TV is 2.75 hours, then after Dr. Sameer surveys a very large number of samples of 100 Cal Poly students, in a random sample of 100 students about 16% of them would watch TV for a number of hours at least as extreme as 3.01 hours in either direction. b. This researcher’s p-value would be smaller, half of to be exact, than the p-value reported in (a). This is because the hypothesis in part (a) was two-sided, while Dr. Elliot’s hypothesis is one-sided. Question 8 2.2.16 a. The variable of interest is the SPF of sunscreens. This variable is quantitative. b. The author’s parameter of interest is the average SPF of sunscreens used by students at her school in the long-term. I will assign the symbol μ to this parameter. c. Null hypothesis: μ = 30 Alternative hypothesis: μ > 30 d. I will assign the symbol n to the number 48, the symbol x̄ to the number 35.29, and the symbol s to the number 17.19. e. No, the data do not come from a random sample because every single person in the author’s school does not have an equal chance of being selected. Since the population is students at the school rather than students at her school taking Introductory Statistics, the sample is not random. f. However, I do think the sample is representative of all students at this school, with regard to SPF of their sunscreens. Sampling bias depends on what is being measured, and I do not think SPF of sunscreen is correlated to whether or not students take Introductory Statistics or not. g. A population for which this sample is surely not representative is students on the swim team at the author’s school.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version