Zach is taller than Matt and Richard is shorter than Zach. Which of the following statements would be most accurate?
2 answers:
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Let 
be the random variable for the weight of any given can, and let 
and 
be the mean and standard deviation, respectively, for the distribution of .
You have
Recall that for any normal distribution, approximately 99.7% of it lies within three standard deviations of the mean, i.e.
. This means 0.3% must lie outside this range, 
. Because the distribution is symmetric, it follows that 
.
Also recall that for any normal distribution, about 95% of it falls within two standard deviations of the mean, so
, which means 5% falls outside, and by symmetry, 
.
Together this means
Solving for the mean and standard deviation gives
and 
.
You have
Recall that for any normal distribution, approximately 99.7% of it lies within three standard deviations of the mean, i.e.
Also recall that for any normal distribution, about 95% of it falls within two standard deviations of the mean, so
Together this means
Solving for the mean and standard deviation gives
Answer: No, the data does not support the claim at 1% level as the mean time is no longer than 4.5 years.
Step-by-step explanation:
Since we have given that
n the California state university system take 4.5 years, on average, to finish their undergraduate degrees.
So, the hypothesis would be
Mean = 5.1
Standard deviation = 1.2
n = 49
So, test statistic value would be
At 1% level of significance, critical value is 2.58
Since 2.58>-3.53.
So, we will accept the null hypothesis.
Hence, No, the data does not support the claim at 1% level as the mean time is no longer than 4.5 years.