1) A random sample of 36 adult females is selected from a population with mean h
ID: 3160106 • Letter: 1
Question
1) A random sample of 36 adult females is selected from a population with mean height 65 inches and standard deviation 5 inches. Find the probability that the sample mean height for these 36 adults exceeds 66 inches.
2) Consider the variables X=years of experience, and Y= annual salary. Suppose that a regression equation relating these variables is Y = 33000 + 2000 X.
a) In the context of this problem, what does the value of the y-intercept represent?
b) In the context of this problem, what does the value of the slope represent?
3) Discuss the difference(s) and the relationship(s) between , m, and
4) A professor wishes to estimate the proportion of WVU students who reside outside of WV. He randomly selects 400 students and finds that 160 are out-of-state students (i.e., not WV residents). Construct a 99% confidence interval for the proportion of out-of-state students attending WVU. Interpret your result.
5) The SAT verbal scores were recorded for a random sample of 36 students was selected from High School X and a random sample of 64 students was selected from High School Y. The sample mean and sample standard deviation for each group is given below. Construct a 90% confidence interval for the difference mx - my. Interpret your result.
Sample Number Mean Std. Dev.
High School X 36 585 25.6
High School Y 64 560 24.8
6) A certain type of rod is manufactured to have mean length 15 cm. A researcher obtains a random sample of 50 rods. She wants to test the null hypothesis H0: µ= 15 against the alternate hypothesis HA: µ 15. The sample mean length of the 50 rods is 16.2 cm with a sample standard deviation of 2.3 cm. Explain why the researcher must continue the hypothesis test, i.e., why can she not conclude that the alternate hypothesis is supported by the data.
7) A WVU spokesman states that the mean distance of WVU students’ hometowns to Morgantown is about 200 miles. A group of college students suspects that the average is higher. Data from a random sample of 64 students is collected. The sample mean for these 64 students is 220 miles with a standard deviation of 49.6 miles. Perform a test of hypothesis to determine whose claim is supported by the data. Use a = 0.05 .
8) At WYX supermarket, a random sample of 64 customers used a self-service checkout, and a random sample of 36 customers used a cashier to checkout. Perform a test of hypothesis to determine if there is a difference between mean checkout times. Use a = 0.05.
Sample Number Mean Time (minutes) Std. Dev.
Self-service checkout (Group X) 64 6.25 3.50
Cashier checkout (Group Y) 36 7.80 4.60
9) Compute the sample Pearson Correlation coefficient for X and Y. Interpret your result. Summary information is provided below:
Sx = 142 Sx2 = 2085 Sy = 167 Sy2 = 2898 Sxy = 2435 n = 10
10) 60% of all cumulo-nimbus clouds seeded with silver iodide will produce rain. Suppose that 20 cumulo-nimbus clouds are seeded with silver iodide. Find the probability that 8 or more of these clouds will produce rain.
12) Consider the following situation: A Stat215 student has missed a regularly scheduled exam. The Stat215 instructor must decide between the null hypothesis "The student's excuse for missing the exam is valid" and the alternate hypothesis "The student does not have a valid excuse for missing the exam".
a) In the context of this problem, determine what a TYPE I error is.
b) In the context of this problem, determine what a TYPE II error is.
Explanation / Answer
1.
We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as
x = critical value = 66
u = mean = 65
n = sample size = 36
s = standard deviation = 5
Thus,
z = (x - u) * sqrt(n) / s = 1.2
Thus, using a table/technology, the right tailed area of this is
P(z > 1.2 ) = 0.11506967 [ANSWER]
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