Texts: 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, μ = $2,089 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 = $1,993 with sample standard deviation s = $222. Use a 1% level of significance to test the claim that the monthly mean spending of college students is less than $2,089.
(a) What is the level of significance? State the null and alternate hypotheses (in dollars). (Enter != for ≠ as needed.)
H0: μ = $2,089
H1: μ < $2,089
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. (Multiple Choice)
The Student's t, since the sample size is large and σ is unknown.
Compute the appropriate sampling distribution value of the sample test statistic. (Round your answer to two decimal places.)
?
(c) Estimate the P-value.
P-value > 0.25
0.10 < P-value < 0.25
0.05 < P-value < 0.10
0.01 < P-value < 0.05
P-value < 0.01
Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? (Multiple Choice)
At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application. (Multiple Choice)
There is insufficient evidence, at the 0.01 level, to conclude that the monthly mean spending of college students is less than $2,089.
There is sufficient evidence, at the 0.01 level, to conclude that the monthly mean spending of college students is less than $2,089.