Hi Please solve all of these questions. and please show the steps and give reaso

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Hi Please solve all of these questions. and please show the steps and give reasons for the question . Thank u very much!

Question 5 (1 mark) A pharmaceutical manufacturer wants to determine the proportion of patients that will experience severe side effects when taking their new anti-depressant. In a random sample of 330 patients on the new anti-depressant, 83 experienced severe side effects Construct a 99% confidence interval for the true proportion of patients that will experience severe side effects when taking the new anti-depressant using the large sample confidence interval formula. 282 645 960 2.325 2.576 3.090 (tail area) 0.1 0.05 0.025 0.01 0.005 0.001 %ile 95 97.5 99 99.5 99.9 Your answers can be rounded to three decimal digit accuracy when entered Lower lim Upper lim it is Question 6 (1 mark) The yields for the last five batches from a chemical reactor are 54.41, 56.64, 56.77, 54.67, 53.65 Assuming that these yields form a random sample from a normal population, but sample size is too SMALL to assume s a, construct a 99% confidence interval for the true mean yield. t-values for tail area a v 0.100 0.050 0.025 0.010 0.005 3.078 6.3 4 12.706 31.821 63.657 886 2.920 4.303 6.9655 9.925 638 2,353 182 4.54 5.84 533 2,132 2,776 3,747 4,604 5 1.476 2.015 2.571 3.365 4.03 440 943 2.447 3.143 3.707 415 895 2.365 2.998 3.499 397 1.860 2.306 2.896 3.355 383 1.833 2.262 2.82 3.250 01.372 1,812 2.228 2.764 3.169 Your answers can be rounded to three decimal digit accuracy when entered Lower limi Uppe it is Question 7 (1 mark) The drying time of a certain type of paint under specified test conditions is known to be normally distributed with mean value 74 min and standard deviation 9.8 min Chemists have proposed a new additive designed to decrease average drying time It is believed that drying times with this additive will remain normally distributed with standard deviation 9.8 min. Because of the expense associated with the additive evidence should strongly suggest an improvement in average drying time before such a conclusion is adopted. Let u be the true average drying time when the additive is used. The hypothesis p 74 ver us Ha:M: 74 Ho are to be tested using a random sample of 21 observations. The rejection region is Find the minimum value of c that yields a test with significance 0.1? 960 2.325 2.576 3.090 282 645 o(tail area) 0.1 0.05 0.025 0.01 0.005 0.00 %ile 95 97,5 99 99.5 99.9 Your answer can be rounded to four decimal digit accuracy when entered

Explanation / Answer

(5)

n = 330    

p = 83/330 = 0.251515152    

% = 99    

Standard Error, SE = {p(1 - p)/n} =    (0.251515151515152(1 - 0.251515151515152))/330 = 0.023884525

z- score = 2.575829304    

Width of the confidence interval = z * SE =     2.57582930354892 * 0.0238845252344935 = 0.06152246

Lower Limit of the confidence interval = P - width =     0.251515151515152 - 0.0615224600003619 = 0.18999269

Upper Limit of the confidence interval = P + width =     0.251515151515152 + 0.0615224600003619 = 0.31303761

The 99% confidence interval is [0.19, 0.31]

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