a. if the null hypothesis is true (avg. anxiety level score of children in the sample is the same as the avg. nationwide score; mu = 100), what can you say about the distribution of x-bar among simple random samples of 46 children? b. calculate the p-value on this distribution. given the p-value, what conclusions can you draw?
a.
Based on the central limit theorem when the sample size is sufficiently large and has the population mean of and population standard deviation then the distribution of sample mean is approximately normal.
In the study of anxiety levels of children, the population mean is and population standard deviation . Also, the random sample of 46 children is considered which is sufficiently large . This shows that, the sample distribution of would have normal distribution.
Thus, the distribution of among simple random samples of 46 children is normal.
b.
let denotes the population average anxiety level score of children.
The hypothesis for the claim that the population average anxiety level score of children might be higher than 100 is stated as,
Null hypothesis:
There is no sufficient evidence that the population average anxiety level score of children might be higher than 100.
Null hypothesis:
There is sufficient evidence that the population average anxiety level score of children might be higher than 100.
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