the burning rates of two different solid-fuel propellants used in aircrew escape systems are being studied. it is known that both propellants have approximately the same standard deviation of burning rate; that is, o_1=o_2=3 cm/s. a) test the hypothesis that both propellants have the same mean burning rate. use a fixed level test with a=0.05 and choose the appropriate conclusion from below: b) what is the P-value of the test in part (a)
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05\) - We want to test if the mean burning rates are the same. Let \(\mu_1\) = mean burning rate of propellant 1 Let \(\mu_2\) = mean burning rate of propellant 2 Hypotheses: \(H_0: \mu_1 = \mu_2\) (means are equal) \(H_a: \mu_1 \neq \mu_2\) (means are Show more…
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The burning rates of two different solid-fuel propellants used in aircrew escape systems are being studied. It is known that both propellants have approximately the same standard deviation of burning rate; that is, ̑1=̑2=3 cm/s. From a random sample of size n1=20 and n2=20, we obtain x̄1=18.02 cm/s and x̄2=24.31 cm/s. Test the hypothesis that both propellants have the same mean burning rate. Use a p-value test with ̑=0.05.
Ajiboye T.
The burning rates of two different solid-fuel propellants used in aircrew escape systems are being studied. It is known that both propellants have approximately the same standard deviation of burning rate; that is $\sigma_{1}=\sigma_{2}=3$ centimeters per second. Two random samples of $n_{1}=20$ and $n_{2}=20$ specimens are tested; the sample mean burning rates are $\bar{x}_{1}=18$ centimeters per second and $\bar{x}_{2}=24$ centimeters per second. (a) Test the hypothesis that both propellants have the same mean burning rate. Use $\alpha=0.05 .$ What is the $P$ -value? (b) Construct a $95 \%$ confidence interval on the difference in means $\mu_{1}-\mu_{2} .$ What is the practical meaning of this interval? (c) What is the $\beta$ -error of the test in part (a) if the true difference in mean burning rate is 2.5 centimeters per second? (d) Assuming equal sample sizes, what sample size is needed to obtain power of 0.9 at a true difference in means of $14 \mathrm{~cm} / \mathrm{s} ?$
Statistical Inference for Two Samples
Inference on the Difference in Means of Two Normal Distributions, Variances Known
The burning rates of two different solid-fuel propellants used in aircrew escape systems are being studied. It is known that both propellants have approximately the same standard deviation of burning. Random samples of the propellants are tested, and the sample mean burning rates are measured. The first sample mean burning rate is denoted as X1, and the second sample mean burning rate is denoted as X2. (a) Test the hypothesis that both propellants have the same mean burning rate. Use a significance level of 0.05. What is the p-value? (b) Construct a 95% confidence interval on the difference in means, denoted as L1 - L2. (c) What is the error of the test in part (a) if the true difference in mean burning rates is 2.5 centimeters per second? (d) Assuming equal sample sizes, what sample size is needed to obtain a power of 0.9 at a difference in means of 2.5 cm/s? (a) The null hypothesis is rejected. The p-value is [Round your answer to two decimal places]. (b) The 95% confidence interval is [Round your answer to two decimal places]. (c) The error of the test in part (a) is [Round your answer to five decimal places]. (d) The required sample size is [Round your answer to the next integer].
Madhur L.
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