A large city newspaper periodically reports the mean cost of dinner for two people at restaurants in the city. The newspaper sta
1 answer:
Answer: C) 133
Step-by-step explanation:
The formula to find the sample size is given by :-
, where z* = Critical z-value
= Population standard deviation for prior study.
E= Margin of error.
As per given , we have
E= 5
The critical z-value for 90% confidence level is 1.645.
Substitute al;l the value sin the above formula , we get
Hence, the minimum sample size needed is 133.
Thus , the correct answer is : C) 133
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Answer:
Null hypothesis :
Alternative hypothesis:
And for this case a type of error I for this case would be reject the null hypothesis that the population mean is lower or equal than 0.4 when actually is true.
A Type I error would occur if, in fact, μ ≤ 0.4 ppm, but the results of the sampling lead to the conclusion that μ > 0.4 ppm
Step-by-step explanation:
Previous concepts
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
Type I error, also known as a “false positive” is the error of rejecting a null hypothesis when it is actually true. Can be interpreted as the error of no reject an alternative hypothesis when the results can be attributed not to the reality.
Type II error, also known as a "false negative" is the error of not rejecting a null hypothesis when the alternative hypothesis is the true. Can be interpreted as the error of failing to accept an alternative hypothesis when we don't have enough statistical power
Solution to the problem
For this case we are trying to check the following hypothesis:
Null hypothesis :
Alternative hypothesis:
And for this case a type of error I for this case would be reject the null hypothesis that the population mean is lower or equal than 0.4 when actually is true.
A Type I error would occur if, in fact, μ ≤ 0.4 ppm, but the results of the sampling lead to the conclusion that μ > 0.4 ppm