Question 1160306: i need your help this is statics questions
1.A restaurant tells its customers that the average cost of a dinner there is birr 92 with a standard deviation of birr8.5. a group of concerned customers thinks that the average cost is higher. In order to test the restaurants claim, 100 customers purchase a dinner at the store and find the mean price is birr92.80. Perform a hypothesis test at 0.05 significance level and state the decision.
2You fit a regression line to data that measures the dependent variable weight, on an independent variable, calories eaten. The line is as follows: y= 145+0.005x.
1.Interpret the slope of the line
2.Interpret the intercept of the line. Does the intercept interpretation make sense in this problem?
3.A95% confidence interval for a population mean was reported to be 152 to 160. If σ 2 15, what sample size was used in this study?
4.A researcher reports survey results by stating that the standard error of the mean is 20. The population standard deviation is 500.
a. How large was the sample used in this survey?
b. What is the probability that the point estimate was within 25 of the population mean?
5.In an effort to estimate the mean amount spent per customer for dinner at an Koket restaurant, data were collected for a sample of 49 customers. The data collected are shown in the CD file named Restaurant. Based upon past studies the population standard deviation is assumed known with σ 2 birr55.
a. At 95% confidence, what is the margin of error?
thanks more for your help.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! With appropriate assumptions including random sampling,
Ho: price is < =92
Ha: it is >92
alpha=0.05 p{reject Ho|Ho true|
test statistic is a z(0.95, df=99) The sd is given for the population
critical value z>1.645
z=(92.80-92)/8.5/sqrt(100)
=0.94
fail to reject Ho; insufficient evidence to say the mean price is >92 birr
The y-intercept is the weight of a person who doesn't consume any calories. That makes no sense, but intercepts in many regression lines are far from the data points and may make no sense.
The slope of the line is weight per calories eaten, and suggests that weight increases 1 pound per every 200 cal in the diet eaten (200*0.005=1). This suggests that as people consume more and more calories on a daily basis their weight rises. That in itself is qualitatively true, but the number of calories we consume on a daily basis is from 0 (sick or fasting) to maybe a few thousand unless somebody has a job or exercise leading to consuming of many thousands of calories. In other words, the effective domain is limited.
The half-interval is 4 = z*sigma/sqrt(n)
4 sqrt(n)=z*sigma=1.96*215
sqrt(n)=1.96*215/4=105.35
n=11,099 rounding up
SEM=z*sigma/sqrt(n)=20. z is not given, so will assume it is 1.96
1.96*500/sqrt(n)=20
1.96*500/20=sqrt(n)=49
n=2401
The SEM is 20, the point estimate will be within 25 meaning it will be with 1.25 sd of the mean with 0.7887 probability.
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