I really need a great grade on this coming exam to be able to get through the class. I have these practice problems and I've been running into some trouble on some of them. I was hoping some of you could run me through some of these.
1.) A psychologist is studying the distribution of IQ scores of girls at an alternative high school. In wishing to test the following hypotheses about the average IQ scores in this school, the psychologists takes a random sample of nine girls. The sample mean IQ score for these nine girls is 114. Assume that IQ scores follow a normal distribution with the population standard deviation σ = 15. For the hypothesis given below, calculate the p-value.
H0: μ = 100 vs. H1: μ ≠ 100
Give your answer accurate to four decimals places.
Answer: 0.0052
2.) A government report gives a 99% confidence interval for the mean family income as ($134.87 ,$155.69).This result was calculated based on a simple random sample of 188 households from a large normal population with known population standard deviation. Find σ, the population standard deviation. Give your answer accurate to two decimal places.
Answer: 55.41
3.) A driving instructor is interested in determining the mean braking reaction for the population of female high school students taking a driving instruction class. A sample of 129 female students yields the following results: a sample mean of 0.65 seconds, and a sample variance of s2=30 seconds.
For a 95% confidence interval for the population mean μ what will be the half-width of the interval? Please give your answer accurate to two decimal places.
Answer: 0.95
4.) If X ~ t16, then what is P(X > -1.746)
Answer: .95
5.) For a recent exam given in your statistics class, the average score for the 170 students in the class was 18, with a standard deviation of sX = 4. If the professor makes the following correction to the score: Y = 3 + 3X, then what is the mean of the random variable Y?
Answer: 57