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DBA7310 Week Six Assessment

# DBA7310 Week Six Assessment - Question 1 A random sample of...

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Question 1: A random sample of 18 young adult men (20-30 years old) was taken. Each man was asked how many minutes of sports they watched on television daily. It is known that the STD = 10. Test to determine at the 5% significance level whether there is enough statistical evidence to infer that the mean amount of television watched daily by all young adult men is greater than 50 minutes? Z-Test: Mean Mean 59.166 7 Standard Deviation 9.9425 Observations 18 Hypothesized Mean 1 SIGMA 10 z Stat 24.678 P(Z<=z) one-tail 0 z Critical one-tail 1.6449 P(Z<=z) two-tail 0 z Critical two-tail 1.96 Yes, there is enough statistical evidence to infer that the mean mount of television watched daily by young men is greater than 50 minutes. Question 2: A statistics practitioner would like to estimate a population mean to within 50 units with 99% confidence given that the population standard deviation is 250. ^ = exponent A) What sample size should be used? n = (2.576^2 * 250^2)/50^2 n = (6.636* 62500)/2500 n = 165.89 which rounds up to a sample size of 166 (Rounding up) n = 166 B) Repeat part (a) with a standard deviation of 50: n = (z^2 * σ^2)/c^2 n = (2.576^2 * 50^2)/50^2 n = (6.636* 2500)/2500 n = 6.64

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(Rounding up) n = 7 C) Repeat part (a) using a 95% confidence level: n = (z^2 * σ^2)/c^2 n = (1.96^2 * 250^2)/50^2 n = (3.842* 62500)/2500 n = 96.04 (Rounding up) n = 97 D) Repeat part (a) when we wish to estimate the population mean to within 10 units: n = (z^2 * σ^2)/c^2 n = (2.576^2 * 250^2)/10^2 n = (6.636* 62500)/100 n = 4147.36 (Rounding up) n = 4148 Question 3: Some traffic experts believe that the major cause of highway collisions in the differing speeds of cards. That is when some cars are driven slowly while others are driven at speeds well in excess of the speed limit, cars tend to congregate in bunches, increasing the probability of accidents. Thus the greater the variation in speeds, the greater will be the number of collisions that occur. Suppose that one expert believes that when the variance exceeds 18mph, the number of accidents will be unacceptably high. A random sample of the speeds of 245 cars on a highway with one of the highest accident rates in the country is taken. Can we conclude at the 10% significance level that the variance in speeds exceeds
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