I need help with my statistics questions. they are attached below with all the information. THIS IS NOT AN EXAM OR QUIZ

Suppose a study was conducted to compare the sleep deprivation rates of Californians and Oregonians. The proportion of California residents who reported insufficient rest or sleep during each of the preceding 30 days is 8.8%, while this proportion is 7% for Oregon residents. These data are based on simple random samples of 1,545 California and 1,460 Oregon adult residents. a) Conduct a hypothesis test to determine if these data provide strong evidence the rate of sleep deprivation is different for the two states. Use California as Group A and Oregon as Group B. Test statistic (Round to 4 decimal places): p-value (round to 4 decimal places): 0" Conclusion at the 5% level of si-nificance: Q) We fail to reject the null hypothesis. 0 We accept the null hypothesis. Q We reject the null hypothesis. 046 b) It is possible the conclusion of the test in part (a) is incorrect (contradicts with the reality). If this is the case what t e of error was made? O A combination of Type | and a error C Type III Error Type II Error C Type o error 0 Type | Error Carolina, a researcher in psychology and biobehavioral health, believes that city residents and residents of rural areas differ in how appealing they find owning a cat. A random sample of 123 people who live in New York City were surveyed and 43 identified themselves as a "cat person." A random sample of 115 people who live in the surrounding rural area were selected and 53 identified themselves as a "cat person." Conduct an appropriate hypothesis test at the a = 0.05 significance level to test Carolina's claim. Round answers to 4 decimal places where appropriate. a. State the null and alternative hypotheses. Ho : P. V V of E V V o P, V V HA : P, V V OF F V V o p , V v . b. What is the appropriate distribution to use for the hypothesis test? Z (Normal) c. Find the test statistic. Test Statistic: d. Determine the P-value: P-value: e. What decision results from the test? | Fail to reject the null hypothesis. Vv https://barstow.instructure.com/courses/1 1409/assignments/232349 1/8 11/26/22, 12:33 PM Chapter 10 Hypothesis Tests with Two Samples f. INTERPRET the conclusion in the context of the problem; e.g., explain in words what the result of the test means. The evidence disproves the claim that city residents and residents of rural areas differ in how appealing they find owning a cat. The data are statistically significant at a = 0.05. The test results are inconclusive. No conclusion can be made about whether city residents and residents of rural areas differ in how appealing they find owning a cat. There is evidence to support the claim that city residents and residents of rural areas differ in how appealing they find owning a cat. The data are statistically significant at a = 0.05. There is insufficient evidence to support the claim that city residents and residents of rural areas differ in how appealing they find owning a cat. The data are not statistically significant at x = 0.05.A random sample of m = 264 people who live in a city were selected and 117 identified as a cat person. A random sample of m = 118 people who live in a rural area were selected and 55 identified as a cat person. Find the 95% confidence interval for the difference in the proportion of people that live in a city who identify as a cat person and the proportion of people that live in a rural area who identify as a cat person. Round answers to 2 decimal places, use confidence interval notation : (_ , _) S You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. You sample 40 night students, and the sample mean GPA is 2.06 with a standard deviation of 0.3. You sample 25 day students, and the sample mean GPA is 2.03 with a standard deviation of 0.36. Test the claim using a 5% level of significance. Assume the population standard deviations are unequal and that GPAs are normally distributed. Give answer to at least 4 decimal places. What are the correct hypotheses? Ho_v 6* = o' H1_ cf - d, o Based on the hypotheses, find the following: Test Statistic = p value = The correct decision is to Fail to reject the null hypothesis v V c)\"6 The correct summary would be: There is not enough evidence to support the claim v V' d' that the mean GPA of night students is different from the mean GPA of day students. You are testing the claim that smiling, rather than remaining neutral, during a court proceding will lead to a different punishment from the judge. A sample of 34 people who smiled during their hearing and 34 people who kept neutral facial expressions during their hearing is taken and each judgment was rated for leniency. Those who smiled (population 1) had a mean leniency rating of 4.9 with a standard deviation of 1.7, while those who did not smile (population 2) had an average leniency rating of 4.1 and standard deviation 1.5. Test the claim using a 10% level of significance. What are the correct hypotheses? HUI\" 6' I\" d\" I\" 0' HaI\" 0' I\" 0' I\" 6' Based on the hypotheses, find the following: Test Statistic = p-value = The correct decision is to reject the null hypothesis v V 0' . The correct summary would be: There is enough evidence to support the claim V '/ 0' that there is a difference in leniency when smiling over being neutral when in trouble. LeFrance, M. and Hecht, M.A., "Why Smiles Generate Leniency", Personality and Social Psychology Bulletin. 1995; 21:207-204. abstract Test the claim that the mean GPA of night students (un) is significantly different than the mean GPA of day students (up) at the 0.02 significance level. The null and alternative hypothesis would be: Ho: UN 2 UD HO: UN MD H1: IN # ND The test is: left-tailed right-tailed two-tailed of The sample consisted of 60 night students, with a sample mean GPA of 2.55 and a standard deviation of 0.08, and 60 day students, with a sample mean GPA of 2.56 and a standard deviation of 0.04. The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals) Based on this we: O Reject the null hypothesis Fail to reject the null hypothesisSome people believe that different octane gasoline result in different miles per gallon in a vehicle. The following data is a sample of 11 people which were asked to drive their car only using 10 gallons of gas and record their mileage for each 87 Octane and 92 Octane. 237 238 229 224 119 297 351 241 186 209 11 .- n II II -- 562 Do the data support that different octanes produce different miles per gallon at the a = 0.02 level of significance? Note: A normal probability plot of difference in car mileage between Octane 37 and Octane 92 indicates the population could be normal and a boxolot indicated no outliers. httpso'i'bnrslowinslruclurccoml'courscsl] [miassignnlcnls32349 I \"2602. I134 PM Chapter I0 Hypothesis Tcsls with Two Samples a. Express the null and alternative hypotheses in symbolic form for this claim. Assume pg = m p52, where in is the population mean mileage for Octane 87 and a2 is the mean mileage for Octane 92. H0 : d =0 Vm '/ 04 prg #0 V'd' b. What is the significance level? a : c. What is the test statistic? Round to 3 decimal places. -v= d. What is the p -value? Round to 5 decimal places. p = e. Make a decision. Q) Do not reject the null O Reject the null d\" \\l e. Make a decision. (Q Do not reject the null O Reject the null on J f. What is the conclusion? Q There is Sufficient evidence to Support the claim that different octanes produce different miles per gallon. (Q There is not sufficient evidence to support the claim that different octanes produce different miles per gallon. Is the average time to complete an obstacle course different when a patch is placed over the right eye than when a patch is placed over the left eye? Eight randomly selected volunteers first completed an obstacle course with a patch over one eye and then completed an equally difficult obstacle course with a patch over the other eye. The completion times are shown below. "Left" means the patch was placed over the left eye and "Right" means the patch was placed over the right eye. Time to Com - lete the Course "I...\" \"Inn-Ill Assume a Normal distribution. What can be concluded at the the or = 0.01 level of significance level of significance? For this study, we should use t-test for the difference between two dependent population means V J o' a. The null and alternative hypotheses would be: H0: pd V " = V V 0 V '/ {please entera decimal) c5\" 0" ct" httpszi'fbnrslow.instruclurc.cnn'u'courscst'] l40'3fassignmcntsf232349 if? I If2t'm'22. I234 PM Chapter IO Hypothesis Tcsls with Two Samples 0 I ,- I Ha ' pd V V E f' 0 V V Please enter a decimal) 0" o\" o' b. The test statistic t V V {please show your answer to 3 decimal places.) 0' c. The p-value = (Please show your answer to 4 decimal places.) d. The p-value is a o'5 e. Based on this, we should fail to reject V V the null hypothesis. 0' f. Thus. the final conclusion is that c' f. Thus, the nal conclusion is that O The results are statistically significant at a = 0.01, so there is sufficient evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is not the same as the population mean time to complete the obstacle course with a patch over the left eye. 0 The results are statistically significant at o: = 0.01, so there is sufficient evidence to conclude that the eight volunteers that were completed the course in the same amount of time on average with the patch over the right eye compared to the left eye. 0 The results are statistically insignificant at or = 0.01, so there is statistically significant evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is equal to the population mean time to complete the obstacle course with a patch over the left eye. The results are statistically insignificant at a = 0.01, so there is insufficient evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is not the same as the population mean time to complete the obstacle course with a patch over the left eye. J o' Hint: Hypothesis Testing with Two Samples Do college students enjoy playing sports less than watching sports? A researcher randomly selected ten college students and asked them to rate playing sports and watching sports on a scale from 1 to 10 with 1 meaning they have no interest and 10 meaning they absolutely love it. The results of the study are given below. Playing vs. Watching Sports Data Assume a Normal distribution. What can be concluded at the the a = 0.01 level of significance level of significance? For this study, we should use [ttest for the difference between two dependent population means V1\" a\" a. The null and alternative hypotheses would be: H0: Iud I\" = :71" I0 V {please entera decimal] o" 0" 0" H1: |ud f'