Question

Listed below are time intervals (min) between eruptions of a geyser. Assume that the "recent" times are within the past few years, the "past" times are from around 20 years ago, and that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Does it appear that the mean time interval has changed? Is the conclusion affected by whether the significance level is 0.10 or 0.01? Recent 78 90 90 78 57 101 63 87 70 87 81 84 55 81 74 102 60 O 88 87 93 94 64 86 84 92 86 91 90 91 Past Let u, be the recent times and let u, be the past times. What are the null and alternative hypotheses? Ов. Н Н «р2 O A. Ho: H H2 H: H1 = H2 H: H, =H2 O D. Ho H1=H2 O C. Ho: H1=H2 H: H >H2 Calculate the test statistic. t= -0.68 (Round to two decimal places as needed.) Find the P-value. P-value = (Round to three decimal places as needed.) Make a conclusion about the null hypothesis and a final conclusion that addresses the original claim. Use a significance level of 0.10. V the significance level. There V sufficient evidence that the mean time interval has changed. V Ho because the P-value is Is the conclusion affected by whether the significance level is 0.10 or 0.01? O A. Yes, the conclusion is affected by the significance level because H, is rejected when the significance level is 0.01 but is not rejected when the significance level is 0.10. O B. No, the conclusion is not affected by the significance level because H, is not rejected regardless of whether a significance level of 0.10 or 0.01 is used. Oc. Yes, the conclusion is affected by the significance level because H, is rejected when the significance level is 0.10 but is not rejected when the significance level is 0.01. O D. No, the conclusion is not affected by the significance level because H, is rejected regardless of whether a significance level of 0.10 or 0.01 is used.

Answer 1

An: M, = M2 48+ 90+90 t 78+ 57 +01 +63 +87+ 0+ 87+814 84 + X = mean 81 +74+ 102 + 60 78.7058 881 87 + 93 t94t64+ 86 + 84+92 86+9)+9ot91 87.166 6 - Standesd devíations: (48 - 78.7058)4 (90-*8.7058)*+ (90-78:7058)*+ (+8 - 78.7014)4 101 - 78.90 58 Jt (63-78.70582+(87-8.7o58)2 +170-78.7058)2 +(87-8.7058)24 (81-48.7052+ (84-48.7058)*+ (55- 78.4058)*+ ( 81- 8.7058)² (74-78.570 (6o-78.705812 + ( 10R - 48.7058)+ S, = 14.1 (88 - 87. 1666)4 (89-89.1666)*+ ( 43-89.1666)-+ ( 94-87. 1666 )+ ( 64- 87. 1666 ) (P6-89.1666 )+ ( Py-87.1666)* + ( 92~87.1666)*+ ( Q6-8.66)?→ (91-87.166 )² + (90-83.1666 )2 + ( 91-87.1666)2 1a-1 7,9296

test statiste: 78.7058 - 87.1666 199.9678 62.8785 19 12 = - 2.0518 deguee ot freedom : n,-1 2- 63.8785 i99.9678 12 199.9678 62.8785 17 12-1 d.f.2 25 P- value . This s not sigaificant at P< 0. 05 08 0.10. Reject null hypotheris. cance level . Reject Ho. because P- value is ot figniti There is subbicient evidence that the mean time intervad has changes. - Yes, the con clubion is abbected by the dignificamce level because Ho is rejected ohen the significance level 0.10. but is not rejected ushen the Signiticance level is is 0.01-