Sat Probability and Statistics

A study was done to determine if 12 to 15 year old girls who want to be engineers differ in IQ from the average of all girls. The mean IQ of all girls in this age range is known to be about 100. A random sample of 49 girls who state that they want to be engineers is selected and their IQ is measured. The mean IQ of the girls in the sample is 104.5 with a standard deviation of 15. Does this finding provide evidence, at the 0.05 level of significance, that the mean IQ of 12 to 15 year old girls who want to be engineers differs from the average?

What is the correct definition of the parameter?

• Let μ be the true proportion IQ of girls who want to be engineers

• Let μ be the true mean IQ of all girls

• Let μ be the true mean IQ of 12 to 15 year old girls who want to be engineers

• Let μ be the IQ of 12 to 15 year old girls who want to be engineers

A study was done to determine if 12 to 15 year old girls who want to be engineers differ in IQ from the average of all girls. The mean IQ of all girls in this age range is known to be about 100. A random sample of 49 girls who state that they want to be engineers is selected and their IQ is measured. The mean IQ of the girls in the sample is 104.5 with a standard deviation of 15. Does this finding provide evidence, at the 0.05 level of significance, that the mean IQ of 12 to 15 year old girls who want to be engineers differs from the average?

What are the correct null and alternative hypotheses?

• Ho: μ=100 Ha: μ ≠ 100

• Ho: μ = 104.5 Ha: μ ≠ 104.5

• Ho: μ=100 Ha: μ > 100

• Ho: μ ≠ 100 Ha: μ = 100

A study was done to determine if 12 to 15 year old girls who want to be engineers differ in IQ from the average of all girls. The mean IQ of all girls in this age range is known to be about 100. A random sample of 49 girls who state that they want to be engineers is selected and their IQ is measured. The mean IQ of the girls in the sample is 104.5 with a standard deviation of 15. Does this finding provide evidence, at the 0.05 level of significance, that the mean IQ of 12 to 15 year old girls who want to be engineers differs from the average?

What is the correct t score?

• t = 103.548

• t = 0.043

• t = 0.873

• t = 2.1

A study was done to determine if 12 to 15 year old girls who want to be engineers differ in IQ from the average of all girls. The mean IQ of all girls in this age range is known to be about 100. A random sample of 49 girls who state that they want to be engineers is selected and their IQ is measured. The mean IQ of the girls in the sample is 104.5 with a standard deviation of 15. Does this finding provide evidence, at the 0.05 level of significance, that the mean IQ of 12 to 15 year old girls who want to be engineers differs from the average?

What is the correct p-value? The correct t-score was 2.1.

• p-value = 0.0205

• p value = 0.041

• p value = 0.9795

• p value = 0.185

A study was done to determine if 12 to 15 year old girls who want to be engineers differ in IQ from the average of all girls. The mean IQ of all girls in this age range is known to be about 100. A random sample of 49 girls who state that they want to be engineers is selected and their IQ is measured. The mean IQ of the girls in the sample is 104.5 with a standard deviation of 15. Does this finding provide evidence, at the 0.05 level of significance, that the mean IQ of 12 to 15 year old girls who want to be engineers differs from the average?

What is the correct decision? The correct p-value was 0.041

• Since my p-value is greater than α, I fail to reject Ho.

• Since my p-value is greater than α, I reject Ho.

• Since my p-value is less than α, I reject Ho.

• Since my p-value is less than α, I fail to reject Ho.

A study was done to determine if 12 to 15 year old girls who want to be engineers differ in IQ from the average of all girls. The mean IQ of all girls in this age range is known to be about 100. A random sample of 49 girls who state that they want to be engineers is selected and their IQ is measured. The mean IQ of the girls in the sample is 104.5 with a standard deviation of 15. Does this finding provide evidence, at the 0.05 level of significance, that the mean IQ of 12 to 15 year old girls who want to be engineers differs from the average?

What is the correct conclusion?

• There is evidence that the true mean IQ of girls ages 12 to 15 who want to be engineers is equal to 100.

• There is evidence that the true mean IQ of girls ages 12 to 15 who want to be engineers is not equal to 100.

• There is no evidence that the true mean IQ of girls ages 12 to 15 who want to be engineers is not equal to 100.

• There is no evidence that the true mean IQ of girls ages 12 to 15 who want to be engineers is not equal to 100.

The average SAT score at Hormone High School over the years is 520. The mathematics faculty believes that this year’s class of seniors is the best the school has ever had in mathematics. One hundred seventy-five seniors take the exam and achieve an average score of 531 with a sample standard deviation of 96. Does this performance provide good statistical evidence that this year’s class is, in fact, superior? Use a significance level of 0.01.

What is the correct definition of the parameter?

• Let μ be the true mean SAT score at Hormone High School

• Let μ be the true mean SAT score

• Let μ be the true proportion SAT score at Hormone High School

• Let μ be the mean SAT score at Hormone High School

The average SAT score at Hormone High School over the years is 520. The mathematics faculty believes that this year’s class of seniors is the best the school has ever had in mathematics. One hundred seventy-five seniors take the exam and achieve an average score of 531 with a sample standard deviation of 96. Does this performance provide good statistical evidence that this year’s class is, in fact, superior? Use a significance level of 0.01.

What are the correct null and alternative hypotheses?

• Ho: μ = 520 Ha: μ < 520

• Ho: μ = 520 Ha: μ ≠ 520

• Ho: μ = 531 Ha: μ < 531

• Ho: μ = 520 Ha: μ > 520

The average SAT score at Hormone High School over the years is 520. The mathematics faculty believes that this year’s class of seniors is the best the school has ever had in mathematics. One hundred seventy-five seniors take the exam and achieve an average score of 531 with a sample standard deviation of 96. Does this performance provide good statistical evidence that this year’s class is, in fact, superior? Use a significance level of 0.01.

What is the correct t-score?

• t = 0.009

• t = -1.516

• t = 1.516

• t = -0.009

The average SAT score at Hormone High School over the years is 520. The mathematics faculty believes that this year’s class of seniors is the best the school has ever had in mathematics. One hundred seventy-five seniors take the exam and achieve an average score of 531 with a sample standard deviation of 96. Does this performance provide good statistical evidence that this year’s class is, in fact, superior? Use a significance level of 0.01.

What is the correct p-value of the test? The correct t-score is 1.516.

• p-value = 0.131

• p-value = 0.934

• p-value = 0.067

• p-value = 0.318