Question

1.The following data shows test scores for a sample of statistics students.

83, 64, 84, 76, 84, 54, 75, 59, 70, 63, 80, 84, 73, 68, 52, 65, 90, 52, 95, 36, 78, 61, 59, 84, 95, 47, 87

a. Find a 95% confidence interval for the mean test score for all students.

b. Interpret this 95% CI for the population mean.

c. What is the margin of error?

2. A recent national survey found that high school students watched an average of 6.8 movies per month. A random sample of 36 college students revealed that the mean number of movies watched last month was 6.6 with a standard deviation of 0.5 movies. Use a significance level of0.05 in order to determine if college students watch fewer movies per month on average than high school students.

a. What are the hypotheses?

b. Find the test statistic and p-value.

c. Form a conclusion based on the results of the test.

3. The average miles per gallon (mpg) for a certain model of a minivan is stated to be 21.0 mpg for city driving. A random sample of 49 minivans was selected and resulted in a sample mean of 19.8 mpg and a standard deviation of 3.75 mpg. A consumer group wants to test whether or not this minivan model actually gets 21.0 mpg on average. Use a significance level of 0.01.

a. What are the hypotheses?

b. Find the test statistic and p-value.

c. Form a conclusion based on the results of the test.

4. How many ballers should be sampled if we want to estimate the average height of all men’s college basketball players to within half an inch of the true mean with a confidence level equal to 90%? Assume the standard deviation is approximately 3.2 inches.

Answer 1

1.)

given data

83	64	84	76	84	54	75	59	70	63
80	84	73	68	52	65	90	52	95	36
78	61	59	84	95	47	87

a.) degree of freedom(df)=n-1=27-1=26

critical value at 95% confidence(t)=2.056 (use students t table)

95% confidence interval is given by

b.)

ans:the above 95% confidence interval indicates that the population mean will lie within this interval (64.9664,77.1136)

c.)