Answer:
90%
90% of the teas were caffeinated.
Step-by-step explanation:
Total teas: 63+7= 70
63/70 x 100/1= 90%
90% of the teas were caffeinated.
Answer:
- 9 < t < 5
Step-by-step explanation:
Isolate | t + 2 | by subtracting 4 from both sides
| t + 2 | < 7
Inequalities of the type | x | < a always have a solution of the form
- a < x < a, hence
- 7 < t + 2 < 7 ( subtract 2 from all 3 intervals )
- 9 < t < 5
Answer: 6
That chart is confusing ash, but median just refers to the middle value. Just put them in order (4,4,6,9,12) and then find the middle. In this case it's easy as there are an odd number of values. But if you have another question where there are an odd number, for example (4,4,6,10,12,15) find the two middle numbers, 4 and 9, add them (6+10=16) and then divide by 2 to find the number in between those two. (16/2=8)
Hope this helps!
Answer:
-2
Step-by-step explanation:
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)
