Question

(1 point) Traffic police monitor the speed of vehicles as they travel over a new bridge. The average speed for a sample of 41 vehicles was 81.35 kmvh, with the sample standard deviation being 4.52 km/h. We will assume that the speeds are Normally distributed, and the police are interested in the mean speed. Part a) Since the variance of the underlying Normal distribution is not known, inference here would involve the distrbution. How many degrees of freedom would the relevant t distribution have? Part b) Create a 95% confidence interval for the mean speed of vehicles crossing the bridge. Give the upper and lower bounds to your interval, each to 2 decimal places Part c) The police hypothesized that the mean speed of vehicles over the bridge would be the speed limit, Bokmi. Taking a significance level of 5%, what should infer about this hypothesis? A. We should not reject the hypothesis since the sample mean is in the interval found in (b). OB. We should not reject the hypothesis since 80 km/h is in the interval found in (b). C. We should reject the hypothesis since the sample mean was not 80 kmh. OD. We should reject the hypothesis since 80kmh is in the interval found in (b). OE. We should reject the hypothesis since 80 km/h is not in the interval found in (b) Part d) Decreasing the significance level of the hypothesis test above would select all that apply A.not change the Type I error probability. B. Increase the Type I error probability DC. decrease the Type I error probability D. not change the Type Il error probability DE. cither increase or decrease the Type I error probability

Answer 1

1 - Since 80 km/h is în intervall found i'n by we have given thats Sample size : 4.1. =: Nira poptados a sample mean: 81035 km/h = X Sample standard deviation - 4.52 km/h :: The degrees of foceedom: 0-13 41-1 .40 :: Part 6 The degrees of freedom *°/40) Part 6 The 95% confidence interval for mean speed of vechicles is given by Ť + tn-1,042 * 8 ho t40,0.0542 * 4.52 vao ( 81.35 1 2:021 * 07147) 479.99 82:79) (79.91, 82:39) v). The 95% confidence interval for mean speed of vechicles Crossing the boidge is (79.91°, 82:79) part of Hypothesized mean = llo= 80 km/hu. sa Option B) we should not reject the hypothesis. f Til 81: 35 +

part d) Decreaseng the significance level of the hypothesi's test ablue would c) decsease the Type of I emroo poobability explanation: A Type: I enron is when we geject the nell bypothesis . Lower values of a Caignificance level) make it hadders to reject the pule hypothesis, 50 chgesing lower values of significance level can reduce probability of Type-I enroos