Answer:
a. We reject the null hypothesis at the significance level of 0.05
b. The p-value is zero for practical applications
c. (-0.0225, -0.0375)
Step-by-step explanation:
Let the bottles from machine 1 be the first population and the bottles from machine 2 be the second population.
Then we have , , and , , . The pooled estimate is given by
a. We want to test vs (two-tailed alternative).
The test statistic is and the observed value is . T has a Student's t distribution with 20 + 25 - 2 = 43 df.
The rejection region is given by RR = {t | t < -2.0167 or t > 2.0167} where -2.0167 and 2.0167 are the 2.5th and 97.5th quantiles of the Student's t distribution with 43 df respectively. Because the observed value falls inside RR, we reject the null hypothesis at the significance level of 0.05
b. The p-value for this test is given by 0 (4.359564e-10) because we have a two-tailed alternative. Here T has a t distribution with 43 df.
c. The 95% confidence interval for the true mean difference is given by (if the samples are independent)
, i.e.,
where is the 2.5th quantile of the t distribution with (25+20-2) = 43 degrees of freedom. So
, i.e.,
(-0.0225, -0.0375)
Answer:
30
Step-by-step explanation:
You can divide 50 by 2 which is 25
Then subtract 5
Add 10
And you get your number
It is really simple really ☺️
This is a geometric sequence with a common ratio of -4:
-9*-4=36
36*-4=-144
-144*-4=576
Thus, the 9th term would be equal to:
(-4)^5*576 which is -589824
The exponent 5 comes from the fact that 4 terms have already been displayed and we need 9-4 more terms to get to the 9th term. Since we are multiplying by -4 only, the 5 remains an exponent
Answer:
-19
Step-by-step explanation:
It is a non repeating decimal
Step-by-step explanation: