Question

Question 2 2 marks A population is normally distributed with an unknown mean μ and unknown standard deviation σ. You collect a random sample of 24 measurements with sample mean7-55.9 and standard deviation-7.53. Use this information to answer the questions below (a) [0.5 mark] What is your 95% confidence İnterval for the population mean μ? (b) [1 mark] what is your best estimate for the population standard deviation σ? (c) [0.5 mark] If a fellow enginer tells you that the population mean μ İS S0.1. would you accept his claim? Explain your answer with statistical evidence

Answer 1

"From the Given information on, size of the sample n = 24, sample mean is x = 55.9, sample standard deviation is s = 7.53, and 100 (1 - alpha)% = 95 %. 100 - (1 - alpha) % confidence interval for population mean is [x - t_(alpha/2x - 1). s/ squreroot n, x + t_(alpha/2, x - 1). s/ squreroot n] 95% confidence interval for population mean is [55.9 - 2.069 [7.53/ squreroot 24], 55.9 + 2.069 [7.53/ squreroot 24]] = [52.7198, 59.0802) Therefore, 95% confidence interval for the population mean is (52.7198, 59.0802). The best estimate for the population standard deviation is sigma = squreroot (n - 1)/n s^2 = squreroot (24 - 1)/24 (7.53^2) = 7.37 Null hypothesis H_0: mu = 59.1 Alternative hypothisis H_1: mu notequalto 59.1 Level of significance alpha = 0.05 and the critical values are - t_ 0.05/2 = -2.069 and t_ 0.05/2 = 2.069 for 23 degrees of freedom. The test statistic is t_ cal = x - mu/ s