Question

Answer the following questions using the data given below.Phone Hold Time for Concert Tickets in Seconds (n = 5)Operators (X) Wait Time (Y)4 385 5 335 6 383 7 344 8 288 (a) Choose the correct set of hypotheses for a two-tailed test for a zero slope.a. H0: β1 ≥ 0 vs. H1: β1 < 0b. H0: β1 ≤ 0 vs. H1: β1 > 0c. H0: β1 = 0 vs. H1: β1 ≠ 0abc(b-1) What is the p-value? (Round your answer to 4 decimal places.) p-value (b2) State the 95% confidence interval for the slope. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.) The confidence interval is from to .

Answer 1

a.

H₀:β=0

H₁:β≠0

b.

p-value: 0.2935

95% CI: [-45.91;19.71]

Explanation:

Hello!

You need to make a linear regression test. For this, you have two variables

X: Operators

Y: Wait time

x: 4 ; 5; 6; 7 ; 8

y: 385 ; 335 ; 383 ; 344 ; 288

The linear regression equation:

Yi: α + βxi + εi

a. The Hypothesis for a two-tailed test for the slope is:

H₀:β=0

H₁:β≠0

b.

The statistic is

t= (b-β)/√Sb₂ ~
`t_(n-2)`

I've used a statistic software to calculate the values

b= 10.31

`t_(H0)`= -1.27

p-value= 0.2935

The 95% CI for the slope, using the formula:

b±
`t_(n-2)`*Sb

is,

[-45.91;19.71]

I hope you have a SUPER day!