A professor is trying to determine if her students guessed on a multiple choice question that had four possible answer choices. She expects that if the students guessed, the distribution of answers would be uniform for that question. She compares the observed distribution of answers with the uniform distribution. The professor conducts a chi-square Goodness-of-Fit hypothesis test at the 5% significance level.

The null and alternative hypotheses are:

H0: The student answers have the uniform distribution.
Ha: The student answers do not have the uniform distribution.
The professor calculates the test statistic is χ20=3.128.
Determine the critical value using the following portion of the χ2-table.

To which set of numbers does the number –5 belong? select all that apply. integers natural numbers rational numbers real numbers whole numbers

Questions 9-10. use the table of educational expenditures to answer the questions. k-12 education expenditures population indiana $9.97 billion 6.6 million illinois $28.54 billion 12.9 million kentucky $6.58 billion 4.4 million michigan $16.85 billion 9.9 million ohio $20.23 billion 11.6million 9. if the amount of k-12 education expenses in indiana were proportional to those in ohio, what would have been the expected value of k-12 expenditures in indiana? (give the answer in billions rounded to the nearest hundredth) 10. use the value of k-12 education expenditures in michigan as a proportion of the population in michigan to estimate what the value of k-12 education expenses would be in illinois. a) find the expected value of k-12 expenditures in illinois if illinois were proportional to michigan. (give the answer in billions rounded to the nearest hundredth) b) how does this compare to the actual value for k-12 expenditures in illinois? (lower, higher, same? )

If angle b measures 25°, what is the approximate perimeter of the triangle below? 10.3 units 11.8 units 22.1 units 25.2 units