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(1 point) Physicians at a clinic gave what they thought were drugs to 980 patients. Although the doctors later learned that the drugs were really placebos, 57 % of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patients condition improving is 0.56. Test the hypotheses that the proportion of patients improving is > 0.56. Find the test statistic: Find the pvalue. p: (1 point) An Office of Admission document at a certain university claims that 54.5% of their undergraduates are female. To test this claim, a random sample of 220 undergraduates was selected. In this sample, 51.5% were female. Is there sufficient evidence to conclude that the document's claim is false? Carry out a hypothesis test at a 4% significance level. A. The value of the test statistic is: B. The pvalue is D. Your decision for the hypothesis test: OA. Do Not Reject H0. OB. Reject H1. O C. Reject H0. OD. Do Not Reject H1 . (1 point} Lindsey thinks a certain potato chip maker is putting fewer chips in their regular bags of chips. From a random sample of 22 bags of potato chips she calculated a P value of 0.065 for the sample. (a) At a 5% level of significance, is there evidence that Lindsey is correct? (Type: Yes or No): (b) At a 10% level of significance, is there evidence that she is correct? (Type: Yes or No): (c) In a statistical test of hypotheses, we say that the data are statistically significant at level 0: if CA. the P - value is less than a. O B. the P value is larger than a. 00. a = 0.05. O D. a is small. ('1 point) For each problem, select the best response. (a) In testing hypotheses, which of the following would be strong evidence against the null hypothesis? OA. Obtaining data with a large P value. 0 B. Using a large level of significance. 00. Using a small level of significance. 0 D. Obtaining data with a small P value. (b) The P value of a test of a null hypothesis is OA. the probability the null hypothesis is false. OB. the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed. O C. the probability the null hypothesis is true. O D. the probability, assuming the null hypothesis is false, that the test statistic will take a value at least as extreme as that actually observed. (c) In formulating hypotheses for a statistical test of significance, the null hypothesis is often OA. a statement that the data are all 0. O B. 0.05 O C. a statement of "no effect" or "no difference". 0 D. the probability of observing the data you actually obtained ('1 point) A random sample of 100 observations from a population with standard deviation 14.99 yielded a sample mean of 92.7. 1. Given that the null hypothesis is ,u = 90 and the alternative hypothesis is ,u > 90 using a = .05, find the following: (a) Test statistic = (b) P value: (c) The conclusion for this test is: OA. There is insufficient evidence to reject the null hypothesis 0 B. Reject the null hypothesis 0 0. None of the above 2. Given that the null hypothesis is ,u = 90 and the alternative hypothesis is ,u 75 90 using a = .05, find the following: (a) Test statistic = (b) P - value: (c) The conclusion for this test is: OA. Reject the null hypothesis 0 B. There is insufficient evidence to reject the null hypothesis 0 C. None of the above ('1 point) A noted psychic was tested for ESP. The psychic was presented with 240 cards face down and was asked to determine if the card was one of 5 symbols: a star, cross, circle, square, or three wavy lines. The psychic was correct in 65 cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. Assume the 240 trials can be treated as an SRS from the population of all guesses. To see if there is evidence that the psychic is doing better than just guessing, we test H 0 : p = .2 H a : p > .2 (a) What is the zstatistic for this test? (b) What is the Pvalue of the test? ('1 point) Matt thinks that he has a special relationship with the number 'i. In particular, Matt thinks that he would roll a 1 with a fair 6sided die more often than you'd expect by chance alone. Suppose p is the true proportion of the time Matt will roll a 'i. (a) State the null and alternative hypotheses for testing Matt's claim. (Type the symbol p for the population proportion, whichever symbols you need of "", "'=' " not =" and express any values as a fraction e.g. p = 1/3) H0: H0: (b) Now suppose Matt makes n = 30 rolls, and a '1 comes up 6 times out of the 30 rolls. Determine the Pvalue of the test: Pvalue = (0) Answer the question: Does this sample provide evidence at the 5 percent level that Matt rolls a 1 more often than you'd expect? (Type: Yes or No)