Question

You are testing to see whether there is a difference between how much people spend on food when they're out if they are alone versus if they are with their friends. You want to collect information on the amount of money spent per meal at a particular restaurant for two different groups; for your first sample (represented using number 1), your sample contains 18 meals served to individuals sitting by themselves. For your second sample (represented using number 2), your sample contains 21 meals served to individuals sitting with at least another person. You hypothesize that people tend to spend more on food when they are with company than when they are alone. In other words, you have the alternative hypothesis HA: μ1−μ2<0 H A : μ 1 - μ 2 < 0 . Assuming that the variances for both groups are equal when the null hypothesis is true, calculate the standard error of the difference between sample averages assuming that the standard deviations for the two samples are s1 s 1 = 4.51 and s2 s 2 = 7.25.

Note: 1- Round your intermediate numbers to 4 decimal places. 2- Round you final answer to 3 decimal places. Enter your final answer to 3 decimal places.

Answer 1

The statistical software output for this problem is:

Two sample T summary hypothesis test:
μ₁ : Mean of Population 1
μ₂ : Mean of Population 2
μ₁ - μ₂ : Difference between two means
H₀ : μ₁ - μ₂ = 0
H_A : μ₁ - μ₂ ≠ 0
(with pooled variances)

Hypothesis test results:

Difference	Sample Diff.	Std. Err.	DF
μ1 - μ2	1	1.9737342	37

Hence,

Standard error for the differences = 1.974