1 A soda manufacturer must control the amount of soda in eac

1. A soda manufacturer must control the amount of soda in each bottle Each bottle is supposed to contain 255mL of soda On a given day, a random sample of 25 bottles had mean x = 255.5mL and standard deviation sx = 5.0 mL. What is the true mean soda volume p of the soda at: a) a 98% confidence interval? b) a 95% confidence interval? c) What is the p-value of our measurements under the null hypothesis that says the average volume of a bottle is 2SSmL? (To answer this question. you will need to use Table D backwards- When doing so choose the significance level in the Table that is closest to your t-score.) 2- On average, are people in New York the same height as people in Oregon? Suppose we conducted an experiment to find out. We randomly sample 81 New Yorkers and compute a mean height of x1 = 1.3m, and a standard deviation of s1 = 0.3m In addition, we randomly sample 95 Oregonians and compute a mean height of x2 = 1.1 m, and a standard deviation of s2 = 0.4m a) What is the p-value of our dataset under the null hypothesis that says there is no difference in heights (on average) between people in New York and people in Oregon? Use the largest conservative estimate for the degrees of freedom given in Table D. while choosing the significance level in the Table closest to your t-score Using your exact t-score from part a), can we conclude that people from New York have the same height as people in Oregon at: b) The alpha = 0.001 significance level? c) The alpha = 0.0005 significance level?

Solution

Q1.
1. AT 98% CI
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=255.5
Standard deviation( sd )=5
Sample Size(n)=25
Confidence Interval = [ 255.5 ± t a/2 ( 5/ Sqrt ( 25) ) ]
= [ 255.5 - 2.49 * (1) , 255.5 + 2.49 * (1) ]
= [ 253.01,257.99 ]

2.
AT 95% CI
Confidence Interval = [ 255.5 ± t a/2 ( 5/ Sqrt ( 25) ) ]
= [ 255.5 - 2.06 * (1) , 255.5 + 2.06 * (1) ]
= [ 253.44,257.56 ]

3.
Set Up Hypothesis
Null, H0: U=255
Alternate, H1: U!=255
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =255.5-255/(5/Sqrt(24))
to =0.5
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != 0.5 ) = 0.6216