Question

The Math High School 12 score (MHS12) is a test taken by high school seniors. MHS12 results have a normal distribution with unknown mean $\mu$ and unknown standard deviation $\sigma$. A researcher took a random sample of 29 high school seniors and for each of these, determined the MHS12 score. The following are these scores: 5.5, 8.4, 10.8, 9.2, 11.7, 7.6, 9.8, 6.7, 9.4, 8.2, 9.4, 12.0 7.6, 8.9, 9.6, 8.6, 9.2, 8.6, 7.4 a)Use the data to calculate an unbiased point estimate of the true mean, $\mu$, of MHS12 scores b)Use the data to find an unbiased point estimate of the population variance, $\sigma^2$ of MHS12 scores. c) Use the data to find the maximum likelihood estimate of the population variance, $\sigma^2$, of MHS12 scores. d) Find the sample standard deviation of the above data e) Calculate the Interquartile Range of the above data using the R IQR function. f) Create a 98% confidence interval for $\mu$ based on this data. ( g) What critical value did you use to create the 98% confidence interval in part f)? h)Create a 98% prediction interval for the MHS12 score of the next student selected based on this data. (

          The Math High School 12 score (MHS12) is a test taken by high school seniors. MHS12 results have a normal distribution with unknown mean $\mu$ and unknown standard deviation $\sigma$. A researcher took a random sample of 29 high school seniors and for each of these, determined the MHS12 score. The following are these scores:
5.5, 8.4, 10.8, 9.2, 11.7, 7.6, 9.8, 6.7, 9.4, 8.2, 9.4, 12.0
7.6, 8.9, 9.6, 8.6, 9.2, 8.6, 7.4
a)Use the data to calculate an unbiased point estimate of the true mean, $\mu$, of MHS12 scores
b)Use the data to find an unbiased point estimate of the population variance, $\sigma^2$ of MHS12 scores.
c) Use the data to find the maximum likelihood estimate of the population variance, $\sigma^2$, of MHS12 scores.
d) Find the sample standard deviation of the above data
e) Calculate the Interquartile Range of the above data using the R IQR function.
f) Create a 98% confidence interval for $\mu$ based on this data. (
g) What critical value did you use to create the 98% confidence interval in part f)?
h)Create a 98% prediction interval for the MHS12 score of the next student selected based on this data. (

$The Math High School 12 score (MHS12) is a test taken by high school seniors. MHS12 results have a normal distribution with unknown mean μ and unknown standard deviation σ. A researcher took a random sample of 29 high school seniors and for each of these, determined the MHS12 score. The following are these scores: 5.5, 8.4, 10.8, 9.2, 11.7, 7.6, 9.8, 6.7, 9.4, 8.2, 9.4, 12.0 7.6, 8.9, 9.6, 8.6, 9.2, 8.6, 7.4 a)Use the data to calculate an unbiased point estimate of the true mean, μ, of MHS12 scores b)Use the data to find an unbiased point estimate of the population variance, σ^2 of MHS12 scores. c) Use the data to find the maximum likelihood estimate of the population variance, σ^2, of MHS12 scores. d) Find the sample standard deviation of the above data e) Calculate the Interquartile Range of the above data using the R IQR function. f) Create a 98% confidence interval for $\mu$ based on this data. ( g) What critical value did you use to create the 98% confidence interval in part f)? h)Create a 98% prediction interval for the MHS12 score of the next student selected based on this data. ($

Added by Jeffrey A.

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