Question $5$

Estimating Mean SAT Math Score

The SAT is the most widely used college admission exam. $($Most community colleges do not

require students to take this exam.$)$ The mean SAT math score varies by state and by year, so

the value of $$ depends on the state and the year. But let's assume that the shape and spread of

the distribution of individual SAT math scores in each state is the same each year. More

specifically, assume that individual SAT math scores consistently have a normal distribution

with a standard deviation of $94.$ An educational researcher wants to estimate the mean SAT

math score $()$ for his state this year. The researcher chooses a random sample of $686$ exams in

his state. The sample mean for the test is $483.$

Find the $90\%$ confidence interval to estimate the mean SAT math score in this state for this year.

Use the unrounded values in Excel to find the answers to #$2,$ #$3$ and #$4.$

The $z-$value is

The standard error has a value $o.$

The margin of error has a value of

Find the $90\%$ confidence interval to estimate the mean SAT math score in this state for this year.$($

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one option from each menu.

aby Part $1$: $3$ points

aby Part $2$: $3$ points

ab$)$ Part $3$: $3$ points

ab$)$ Part $4$: $3$ points

aby Part $5$: $3$ points

$15$ points