- Develop the UMP test for testing with n = 2. H₂:0 = 5 VS Ha: 0 < 5 Where 8 is the mean of a Poisson distribution f(x)= = 0%e-9 x = 0, 1, 2, ... x= .05

Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is ? = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 41 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.5 with sample standard deviation s = 3.0. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood. (a) What is the level of significance? State the null and alternate hypotheses. (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. What is the value of the sample test statistic? (c) Estimate the P-value. Sketch the sampling distribution and show the area corresponding to the P-value. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the…

Q1// Choose the correct answer with all explanations 1. The standard deviation of binomial distribution is a. Vnpq b. npq c. np?q с. d. np 2. For two correlated variables x and y, if coefficient of correlation between x and y is 0.8014, variance of x and y are 16 and 25 respectively. Then the covariance between x and y is: a. 162.08 b. 16.028 c. 160.28 d. 16.208 3. In how many ways can we sort the letters of the word MANAGEMENT so that the comparative position of vowels and consonants remains the same as in MANAGEMENT? а. 1280 b. 720 с. 960 d. 1080 4. The normal distribution depends on which of the following? a. Mean and standard deviation b. Sample size and probability of success c. Standard deviation and number of success d. Mean and probability of success 5. The successful life of product, the time, the weight and the height are classified as: a. Continuous random variables b. Discrete random variables c. Continuous waiting time variables d. Continuous hyper geometric variables.

Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is ? = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.8 with sample standard deviation s = 3.1. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.   a) What is the level of significance?   b) What is the value of the sample test statistic? (Round your answer to three decimal places.)