Being a college student is not an easy financial endeavor. In addition to paying for tuition, students also need to pay for rent, food, utilities, etc. This does not even include nonessential discretionary
spending. One study claimed that college students spend, on average, u = $2,083 a month. To determine if this is true, a random sample of 41 college students were surveyed and showed that in a
month they spent a sample mean x= $1,994 with sample standard deviation s = $224. Use a 1% level of significance to test the claim that the monthly mean spending of college students is less than
$2,083.
USE SALT
(a) What is the level of significance?
State the null and alternate hypotheses (in dollars). (Enter != for + as needed.)
Ho: $$ \mu = 2083 $$
H1: $$ \mu < 2083 $$
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The standard normal, since the sample size is large and a is known.
The Student's t, since the sample size is large and a is unknown.
The standard normal, since the sample size is large and a is unknown.
The Student's t, since the sample size is large and a is known.
Compute the appropriate sampling distribution value of the sample test statistic. (Round your answer to two decimal places.)
(c) Estimate the P-value.
OP-value > 0.250
0.100 < P-value < 0.250
0.050 < P-value < 0.100
0.010 < P-value < 0.050
OP-value < 0.010
Sketch the sampling distribution and show the area corresponding to the P-value.
