Question

1. A random sample of 10 Harper College students was asked the question, “How much did you spend on textbooks this semester?” Below are the data of their responses:

Amount Spent ($) 292 240 316 361 449 428 402 286 349 250

1. Construct and interpret a 95% confidence interval for the mean amount spent for textbooks by all Harper College students.

2. What was the margin of error associated with your estimate? Explain its meaning.

3. Follett claims the mean amount spent by students for textbooks is only $280. What does the interval suggest about Follet’s

   claim?

4. Suppose the true population mean is $268 with a standard deviation of $46. If we assume all amounts follow a normal

   distribution, what is the probability the mean amount spent on textbooks by a random sample of 16 students exceeds $290?

Answer 1

= (292 + 240 + 316 + 361 + 449 + 428 + 402 + 286 + 349 + 250)/10 = 337.3

s = sqrt(((292 - 337.3)^2 + (240 - 337.3)^2 + (316 - 337.3)^2 + (361 - 337.3)^2 + (449 - 337.3)^2 + (428 - 337.3)^2 + (402 - 337.3)^2 + (286 - 337.3)^2 + (349 - 337.3)^2 + (250 - 337.3)^2)/9) = 72.888

df = 10 - 1 = 9

At 95% confidence level, the critical value is t_{0.025, 9} = 2.262

The 95% confidence interval is

We are 95% confident that the true mean amount spent for text books lies in the above confidence interval.

Margin of error is

   

  

Since the population mean 280 does not lie in the confidence interval, so we should not support the claim.

P( > 290)

= P(Z > 1.913)

= 1 - P(Z < 1.913)

= 1 - 0.9721

= 0.0279