Question

1.Suppose we want a 99% confidence interval for the average amount spent on books by freshmen in their first year at college. The amount spent has a normal distribution with standard deviation $23.

(a) How large should the sample be if the margin of error is to be less than $5?

2.

A report in a research journal states that the average weight loss of people on a certain drug is 3434 lbs with a margin of error of ±5±5 lbs with confidence level C = 95%. According to this information, the mean weight loss of people on this drug, ?μ, could be as low as 29 lbs.

(a) If the study is repeated, how large should the sample size be so that the margin of error would be less than 2.5 lbs? (Assume ?= 7σ= 7 lbs.)
ANSWER:  

3.

Samples were collected from two ponds in the Bahamas to compare salinity values (in parts per thousand). Several samples were drawn at each site.

Pond 1: 37.01, 36.75, 36.72, 37.03, 37.02, 37.45, 37.54

Pond 2: 38.24, 39.21, 38.66, 38.53, 38.71
Use a 0.050.05 significance level to test the claim that the two ponds have the same mean salinity value.

(a) The test statistic is

Answer 1

Ans 1 a ) using excel we have

Sample Size Determination
Data
Population Standard Deviation	23
Marginal Error	5
Confidence Level	99%
Intemediate Calculations
Z Value	-2.5758
Calculated Sample Size	140.3944	((B9*B4)/B5)^2
Result
Sample Size Needed	141.0000	ROUNDUP(B10, 0)

141 should the sample be if the margin of error is to be less than $5.

Ans 2 )

Sample Size Determination
Data
Population Standard Deviation	7
Marginal Error	2.5
Confidence Level	95%
Intemediate Calculations
Z Value	-1.9600
Calculated Sample Size	30.1170	((B9*B4)/B5)^2
Result
Sample Size Needed	31.0000	ROUNDUP(B10, 0)

the sample size must  be 31 so that the margin of error would be less than 2.5.

Ans 3 ) using excel>data>data analysis>two sample t

we have

t-Test: Two-Sample Assuming Equal Variances
	pond 1	pond 2
Mean	37.07429	38.67
Variance	0.099629	0.12445
Observations	7	5
Pooled Variance	0.109557
Hypothesized Mean Difference	0
df	10
t Stat	-8.23338
P(T<=t) one-tail	4.57E-06
t Critical one-tail	1.812461
P(T<=t) two-tail	9.15E-06
t Critical two-tail	2.228139

a) The test statistic is -8.2333

p value is 0.0000 since p value is less than 0.05 so we reject the  claim that the two ponds have the same mean salinity value.