A random sample of 49 measurements from one population had a sample mean of 16, with sample standard deviation 5. An independent random sample of 64 measurements from a second population had a sample mean of 19, with sample standard deviation 6. Test the claim that the population means are different. Use level of significance 0.01.
Extracted text: (a) What distribution does the sample test statistic follow? Explain. O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. The Student's t. We assume that both population distributions are approximately normal with known standard deviations. O The standard normal. We assume that both population distributions are approximately normal with known standard deviations. (b) State the hypotheses. O Ho: H1 = H2i H1: H1 < m2="" o="" ho:="" h1="H2i" hz:="" h1="" #="" h2="" o="" ho:="" h1="" #="" h2i="" h:="" h1="H2" o="" ho:="" h1="H2i" hz:="" µ1=""> H2 (c) Compute x, - x2. x1 - x, = Compute the corresponding sample distribution value. (Test the difference u, - H2: Round your answer to three decimal places.) (d) Estimate the P-value of the sample test statistic. O P-value > 0.500 O 0.250 < p-value="">< 0.500="" o="" 0.100="">< p-value="">< 0.250="" o="" 0.050="">< p-value="">< 0.100="" o="" 0.010="">< p-value="">< 0.050="" o="" p-value="">< 0.010 (e) conclude the test. o at the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. o at the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. o at the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. o at the a = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. (f) interpret the results. o fail to reject the null hypothesis, there is sufficient evidence that there is a difference between the population means. reject the null hypothesis, there is insufficient evidence that there is a difference between the population means. o reject the null hypothesis, there is sufficient evidence that there is a difference between the population means. o fail to reject the null hypothesis, there is insufficient evidence that there is a difference between the population means. 0.010="" (e)="" conclude="" the="" test.="" o="" at="" the="" a="0.01" level,="" we="" reject="" the="" null="" hypothesis="" and="" conclude="" the="" data="" are="" not="" statistically="" significant.="" o="" at="" the="" a="0.01" level,="" we="" fail="" to="" reject="" the="" null="" hypothesis="" and="" conclude="" the="" data="" are="" not="" statistically="" significant.="" o="" at="" the="" a="0.01" level,="" we="" fail="" to="" reject="" the="" null="" hypothesis="" and="" conclude="" the="" data="" are="" statistically="" significant.="" o="" at="" the="" a="0.01" level,="" we="" reject="" the="" null="" hypothesis="" and="" conclude="" the="" data="" are="" statistically="" significant.="" (f)="" interpret="" the="" results.="" o="" fail="" to="" reject="" the="" null="" hypothesis,="" there="" is="" sufficient="" evidence="" that="" there="" is="" a="" difference="" between="" the="" population="" means.="" reject="" the="" null="" hypothesis,="" there="" is="" insufficient="" evidence="" that="" there="" is="" a="" difference="" between="" the="" population="" means.="" o="" reject="" the="" null="" hypothesis,="" there="" is="" sufficient="" evidence="" that="" there="" is="" a="" difference="" between="" the="" population="" means.="" o="" fail="" to="" reject="" the="" null="" hypothesis,="" there="" is="" insufficient="" evidence="" that="" there="" is="" a="" difference="" between="" the="" population="">