Statistics Project
Question 1
Based on a survey of 1,000 adults by Greenfield Online and reported in a May 2009 USA Today Snapshot, adults 24 years of age and under spend a weekly average of $35 on fast food. If 200 of the adults surveyed were in the age category of 24 and under and they provided a standard deviation of $14.50, construct a 95% confidence interval for the weekly average expenditure on fast food for adults 24 years of age and under. Assume fast food weekly expenditures are normally distributed.
n = 200
X-bar = 35
s = 14.5
% = 95
Standard Error, SE = s/Ön = 14.5 /√200 = 1.025304833
z- Score = 1.959963985
Width of the confidence interval = z * SE = 1.95996398454005 * 1.02530483272049 = 2.009560545
Lower Limit of the confidence interval = x-bar – width = 35 – 2.00956054530703 = 32.99043945
Upper Limit of the confidence interval = x-bar + width = 35 + 2.00956054530703 = 37.00956055
The 95% confidence interval is [$33, $37]
| Confidence interval – mean | ||
| 95% | confidence level | |
| 35 | mean | |
| 14.5 | std. dev. | |
| 200 | n | |
| 1.960 | z | |
| 2.010 | half-width
37.010= upper confidence limit 32.990 lower confidence limit |
|
Question 2
An experiment was designed to estimate the mean difference in weight gain for pigs fed ration A as compared with those fed ration B. Eight pairs of pigs were used. The pigs within each pair were littermates. The rations were assigned at random to the two animals within each pair. The gains (in pounds) after 45 days are shown below:
RationA RationB
65 58
37 39
40 31
47 45
49 47
65 55
53 59
59 51
Assuming weight gain is normal, find the 95% confidence interval estimate for the mean of the differences ?d where d= ration A – ration B.
| Ration A | RationB | d = Ration A – Ration B |
| 65 | 58 | 7 |
| 37 | 39 | -2 |
| 40 | 31 | 9 |
| 47 | 45 | 2 |
| 49 | 47 | 2 |
| 65 | 55 | 10 |
| 53 | 59 | -6 |
| 59 | 51 | 8 |
| μd = | 3.75 | |
| s = | 5.73 |
n = 8
μd = 3.75
s = 5.73
% = 95
Standard Error, SE = s/Ön = 5.73/√8 = 2.025860928
Degrees of freedom = n – 1 = 8 -1 = 7
t- Score = 2.364624252
Width of the confidence interval = t * SE = 2.36462425159278 * 2.02586092809946 = 4.790399881
Lower Limit of the confidence interval = x-bar – width = 3.75 – 4.79039988093825 = -1.04039988
Upper Limit of the confidence interval = x-bar + width = 3.75 + 4.79039988093825 = 8.540399881
The 95% confidence interval is [-1.04, 8.54]
| Hypothesis Test: Paired Observations | |||||||||
| 0.000 | hypothesized value | ||||||||
| 51.875 | mean RationA | ||||||||
| 48.125 | mean RationB | ||||||||
| 3.750 | mean difference (RationA – RationB) | ||||||||
| 5.726 | std. dev. | ||||||||
| 2.024 | std. error | ||||||||
| 8 | n | ||||||||
| 7 | df | ||||||||
| 1.85 | t | ||||||||
| .1064 | p-value (two-tailed) | ||||||||
-1.037 =confidence interval 95 % lower
8.537=confidence interval 95 % upper
4.787 margin of error
References
Robert J & Patricia K, (2007). Elementary statistics, 10th edition Cengage Learning publishers.
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