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	Past
77	88
92	89
89	93
79	94
57	64
101	86
61	85
88	92
70	87
88	91
81	91
84	91
55
82
75
103
62

Calculate the test statistic

t = ???

Find the​ P-value.

P = ???

Make a conclusion about the null hypothesis and a final conclusion that addresses the original claim. Use a significance level of 0.10

????? H0 because the​ P-value is ????? the significance level. There ???? sufficient evidence that the mean time interval has change

Is the conclusion affected by whether the significance level is0.10 or 0.01?

A.

​Yes, the conclusion is affected by the significance level because H0 is rejected when the significance level is 0.01 but is not rejected when the significance level is 0.10

B.

​Yes, the conclusion is affected by the significance level because H0 is rejected when the significance level is 0.10 but is not rejected when the significance level is 0.01

C.

​No, the conclusion is not affected by the significance level because H0 is rejected regardless of whether a significance level of, 0.10 or 0.01 is used.

D.​

No, the conclusion is not affected by the significance level because H0 is not rejected regardless of whether a significance level of 0.10 or 0.01 is used.

Answer 1

Ho :µ1 - µ2 =0

Ha :µ1-µ2 ╪0

mean of sample 1,               x̅1=79.05882

standard deviation of sample 1,s1 = 14.36781

size of sample 1,                     n1=17

mean of sample 2,               x̅2=87.58333

standard deviation of sample 2,s2 = 7.936777

size of sample 2,                     n2=12

difference in sample means = x̅1-x̅2   = -8.5245

std error , SE = √(s1²/n1+s2²/n2) = 4.1704

t-statistic   = ((x̅1-x̅2)-µd)/SE   = -2.0440

$df=\frac{\left ( \frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}} \right )^{2}}{\frac{\left ( s_{1}^{2}/n_{1} \right )^{2}}{n_{1}-1}+\frac{\left ( s_{2}^{2}/n_{2} \right )^{2}}{n_{2}-1}}=25$

p-value = 0.0516

Conclusion:                            p-value<α=0.10 , Reject null hypothesis

Reject H0 because the​ P-value is less than , the significance level. There is sufficient evidence that the mean time interval has change

-------------------------

Yes, the conclusion is affected by the significance level because H0 is rejected when the significance level is 0.10 but is not rejected when the significance level is 0.01