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Suppose that X is the number of successes in
an experiment with 9 independent trials
where the
Find P(X less than 2).
A) 0.0705
B) 0.8388
C) 0.1287
D) 0.1612
E) 0.9165
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- Matt thinks that he has a special relationship with the number 2. In particular, Matt thinks that he would roll a 2 with a fair 6-sided die more often than you'd expect by chance alone. Suppose p is the true proportion of the time Matt will roll a 2. (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) Ho = H₂ = (b) Now suppose Matt makes n = 38 rolls, and a 2 comes up 8 times out of the 38 rolls. Determine the P-value of the test: P-value= (c) Answer the question: Does this sample provide evidence at the 5 percent level that Matt rolls a 2 more often than you'd expect? (Type: Yes or No)(iii) Find (or estimate) the P-value. OP-value > 0.250 O 0.125 < P-value < 0.250 O 0.050 < P-value < 0.125 O 0.025 < P-value < 0.050 O 0.005< P-value < 0.025 OP-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. O -4 -2 0 2 2 M 2 DO Q -2 -2 (iv) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. O At the a= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. (v) Interpret your conclusion in the context of the application. O Fail to reject the null hypothesis, there…what is p(z<?)=0.88
- Sean thinks that he has a special relationship with the number 6. In particular, Sean thinks that he would roll a 6 with a fair 6-sided die more often than you'd expect by chance alone. Suppose pis the true proportion of the time Sean will roll a 6. (a) State the null and alternative hypotheses for testing Sean'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) Ho= Ha (b) Now suppose Sean makes n = 30 rolls, and a 6 comes up 6 times out of the 30 rolls. Determine the P-value of the test, giving your answer to 4 decimal places. Please use 3 decimal places in your test statistic when finding the P-value. P-value = ⠀⠀ (c) Answer the question: Does this sample provide evidence at the 5 percent level that Sean rolls a 6 more often than you'd expect? (Type: Yes or No) 4New York is known as "the city that never sleeps." A random sample of 25 New Yorkers were asked how much sleep they get per night and the sample mean was 7.3 hours. To test if New Yorkers sleep less than 8 hours a night on average (Ho: u = 8 v.s. HA: u < 8, where u is the mean number of hours New Yorkers sleep a night), the P-value is (i) the probability of getting a random sample of 25 New Yorkers that on average sleep 7.3 hours a night, when New Yorkers actually sleep less than 8 hours per night on average. (ii) the probability of getting a random sample of 25 New Yorkers that on average sleep 7.3 hours or less a night, when New Yorkers actually sleep 8 hours per night on average. (iii) the probability that New Yorkers on average sleep 8 hours per night, given that the 25 randomly sampled New Yorkers on average sleep 7.3 hours a night (iv) the probability that New Yorkers on average sleep less than 8 hours per night, given that the 25 randomly sampled New Yorkers on average sleep 7.3…A sample of n = 7 scores has a mean ofM 5. After one new score is added to the sample, the new mean is found to be M 6. What is the value of the new score? (Hint: Compare the values for EX before and after the score was added.)
- Match the following questions with the correct answers. A. 24 B. 0.0929 C. 2 D. 154 E. 3/4 F. 120 select select select select select select 1. If X220, the probability that a man aged x marries at time t from the present is 15dt/(t+x)2. Find the probability that a person aged 20 eventually marries. 2. If X is the number of 6's which appear when 72 dice are thrown, what is the expected value of X²? 3. Suppose only 12% of men in ancient Greece were honest. What is the probability that the first honest man Diogenes Jencounters will be the third man he meets? 4. Find the expected value of the number of times one must throw a die until the outcome 1 has occurred 4 times? 5. Find the variance value of the number of times one must throw a die until the outcome 1 has occurred 4 times? 6. If for a Poisson distribution 2f(0)+f(2)=2f(1), what is the variance of the distribution?Matt thinks that he has a special relationship with the number 2. In particular, Matt thinks that he would roll a 2 with a fair 6-sided die more often than you'd expect by chance alone. Suppose p is the true proportion of the time Matt will roll a 2. (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) Ho p= 1/6 = Ha= p > 1/6 (b) Now suppose Matt makes n = 34 rolls, and a 2 comes up 7 times out of the 34 rolls. Determine the P-value of the test: P-value = | (c) Answer the question: Does this sample provide evidence at the 5 percent level that Matt rolls a 2 more often than you'd expect? (Type: Yes or No) noFor each p value stated below, what is the decision for each if α = .01? Assume that this is the total probability (two tails combined). 19a. p = .1000 a. Reject H0 b. Retain H0 19b. p = .0050 a. Reject H0 b. Retain H0 19c. p = .0250 a. Reject H0 b. Retain H0 19d. p=.0001 a. Reject H0 b. Retain H0
- Iim. 1223. Flip six unfair coins where, for each coin, P(H) = 0.20 and P(T)= 0.80. Let X be the total number of heads. Find P(X = 4), the probability of getting 4 heads. A. 0.04536 %3D B. 0.03536 C. 0.02536 D. 0.01536A sample of n = 20 observations is drawn from a normal population with u = 1100 and o = 180. Find each of the following: A. P(X > 1176) Probability = B. P(X 1063) Probability =