Question

Question 2. (10 points) In Gondor, it is believed that the mean amount of water per day that the Gondorans drink is 1.8 liters. A random sample of 22 Gondorans is observed. The average amount of water they drink per day is 1.62 liters, with a standard deviation of 0.4 liters. Is the mean amount of water that Gondorans drink less than 1.8 liters? Test with 0.025 Question 3. (15 points) In Rohan, the mean amount of water per day that the Rohinim (people of Rohan) drink is not known A random sample of 20 Rohinim is observed. The average amount of water they drink per day is I.S liters, with a standard deviation of 0.45 liters. Based on the samples in question 2 and this question, is the mean amount of water per day that Gondorans drink more than that of the Rohinim? Test with a 0.01. State the assumptions that must be made in the context of this problem Question 4. (15 Points) Now we combine (pool) the sample data of Gondor and Rohan (given in questions 2 and 3). so that N 42. The average of these 42 numbers is 1.4676, and their standard deviation is 0.4245 Is the mean amount of water per day that the Shire people drink more than that of the people living in the combined country of Rohan and Gondor (call it Gonhan)? Test with a -0.01 Question 5. (10 points) It is claimed that 70% of the Roh in im drink more than 1.5 liters of water per day. Among a sample of 70 randomly selected Rohinim M drink more than 1.5 liters per day. What is the smallest number M can be so that the null hypothesis is retained when the claim is tested at a 0.01?

this question are not seperate. they should be solved   at the same time

Answer 1

Q2.

Given that,
population mean(u)=1.8
sample mean, x =1.62
standard deviation, s =0.4
number (n)=22
null, Ho: ?=1.8
alternate, mean amount of water that gondrones drink is less than 1.8, H1: ?<1.8
level of significance, alpha = 0.025
from standard normal table,left tailed t alpha/2 =2.08
since our test is left-tailed
reject Ho, if to < -2.08
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =1.62-1.8/(0.4/sqrt(22))
to =-2.1107
| to | =2.1107
critical value
the value of |t alpha| with n-1 = 21 d.f is 2.08
we got |to| =2.1107 & | t alpha | =2.08
make decision
hence value of | to | > | t alpha| and here we reject Ho
p-value :left tail - Ha : ( p < -2.1107 ) = 0.02348
hence value of p0.025 > 0.02348,here we reject Ho
ANSWERS
---------------
null, Ho: ?=1.8
alternate, H1: ?<1.8
test statistic: -2.1107
critical value: -2.08
decision: reject Ho
p-value: 0.02348
have evidence that mean amount of water that gondrones drink is less than 1.8,