Question

An article in Radio Engineering and Electronic Physics (1980, Vol. 25, pp. 74-79) investigated the behavior of a stochastic generator in the presence of external noise. The number of periods was measured in a sample of 100 trains for each of two different levels of noise voltage, 100 and 150 mV. For 100 mV, the mean number of periods in a train was 7.9 with s1 2.6. For 150 mV, the mean was 6.9 with s2 2.4. Use ? = 0.01 and assume that each population is normally distributed and the two population variances are equal. (a) It was originally suspected that raising noise voltage would reduce mean number of periods. Do the data support this claim? Yes. (b) Calculate a confidence interval to answer the question in part (a) ? 1-H2 2 111.694 .Round your answer to three decimal places (e.g. 98.765)

Answer 1

that sai sing noise voltage will reduce mean no of periods b) Confidence interval (x_1 bar - x_2 bar) plusminus z squareroot s^2_1/n_1 + s^2_2/n_2 (7.9 - 6.9) plusminus 2.58 squareroot 0.067 + 0.057 1 plusminus 2.58 times 0.35 1 plusminus 0.9104 0.0896 to 1.9104 \r\n x_1 bar = 7.9 s_1 = 2.6 n_1 = 100 x_2 bar = 6.9 s_2 = 2.4 n_2 = 150 H_0: mu_1 = mu_2 i.e There is no difference in the noise level on different voltage H_1: mu_1 notequalto mu_2 i.e There is a significant difference in noise level on different voltage z = (x_1 bar - x_2 bar) - (mu_1 - mu_2)/ squareroot s^2_1/n_1 + s^2_2/n_2 = (7.9 - 6.9) - 0/squareroot (2.6)^2/100 + (2.4)^2/100 = 1/ squareroot 0.067 + 0.057 = 1/0.3529 = 2.833 At 99% Z_critical value = 2.58 Since Z_critical < Z_calculated, we reject the null hypothesis, which means
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