Question 9 10 p' In a large university a study was conducted to estimate the mean annual expenditure of its students on textbooks The expenditure eta student may be regarded as a random variable that is normally distributed with a population standard deviation $250, Suppose a random sample of 50 students is drawn and the sample mean is calculated to be $1.000, (a) What is a 95% condence intewal estimate for the population mean? Answer [Sclctt] v (b) Later. it was discovered that there were 65 students whose data had been collected but the researcher omitted the data of 15 of the students by mistake and reported the sample slze was 50. Let K denote a 95% condence interval for the population mean based on the data from all the 65 students Let L be the 95% condence interval obtained in part (a) What can we conclude about K and L'P Answer [Sclctt] v (c) The data for the i5 students who were omitted in part (b) has an average value of $830 Using the information of all the 65 students. what is a 95% condence inteival estimate for the population mean? Answer [53'5\"] V Question 10 4 p' It may be assumed that the time padents spend waiting to consult a doctor in a polyclinic is normallv distributed.A random sample of 5 observations give the following sample statistics: sample mean = 30 minutes and sample variance = 86. Suppose the population variance is unknown, what is a 90\".: condence interval ofthe population mean [1? O 19.55 s M S 37.10 C) 18.40 s M 5 32.97 0 24 34 5 p 5 40.07 0 211o5p538i34 Question 11 8 p' Assume thatthe weight in grams tgi ofappies produced on a farm can be model as a normal random variable with mean equal to 160g and a standard deviation of 25g. (a) Suppose 50 random samples. each with 36 apples are formed. In how many of the 50 samples would you expect the sample mean to be between 155g and 153g? Give you answer to one decimal place. Answer: number of samples = (bl Suppose 5 random samples. each with 36 apples are formed. Compute the probabilitv that exactly 3 ofthe 5 samples will have its sample mean between 155g arid 163g. Give your answerto two decimal places. Answer: probability =