Question

6. An acoustic Doppler velocimeter is usually equipped with a compass and tilt sensors which allows for instantaneous measurements of pitch heading and roll of the instrument, usually at a sampling frequency of 1 Hz. During a deployment, here is a representative set of readings from the heading (true North) over 5 seconds: 0.47°, 0.41°, 0.58,-0.46° and 0.1°. For this case, (a) Compute the sample mean x and sample variances: (b) If true mean u and true variance of of the random variable X (corresponding to the heading) are -0.25º and 0.6° respectively, does x fall within 95% CI of the sample mean?; (c) If u and o- are unknown but a very large sample of measurements (10000) is available with sample mean x = -0.2753° and sample standard deviation 5 = 0.63237, then what is the confidence interval at 90% confidence level of the population mean? [12 points]

Answer 1

Q. No. Here, readings from the heading over xi o.47, o.41 o.S80 S seron Ans 6 -0.46 & 0. sample mean 1.1 O.22 Sample voiance (s2) [Exi- to.947 0.22 J 5-1 n-l 2-022465 know u& 6 then gs % mean, X S, b) If oe hove c.I. forMisampe tneldz o,2246 0.22 o.224-65 ts- o,22+ xt O.220.224 6 o.22t 0.224 61 2.77 6 e2-776 o.0 8 0.49889 1 iS fall whin gse cof the Sampe mean

9o r0 C1. for population mean are anknon The cohen u & 6 2 sample size is lavqe is O.27S3 .64 Z1019 1 35 So.6323 n 10,00O (oms 0.6323 O. 6323 x1.64 0.27S3+ O. 27S3 10,000 0,006 0.2649 C-o.28s6 o Confidenre intesva) fos population The is mean C-0.28s6,-0. 2649)