This question is incomplete, the complete question is;
How does the size of the bowl affect how much ice cream people tend to scoop when serving themselves. At an "ice cream social" people were randomly given either a 17 oz (n=26) or 34 oz bowl (n=22). They were then invited to scoop as much ice cream as they liked. Did the bowl size change the selected portion size? From technology use df = 34.3132.
Here are the summaries;
Small Bowl Large Bowl
n = 26 n = 22
y = 5.07 oz y = 6.58 oz
s = 1.84 oz s = 2.91 oz
Test an appropriate hypothesis and state your conclusion. Assume any assumptions and conditions that you cannot test and sufficiently satisfied to proceed.
Answer:
p-value = 0.0428
at 0.05 significance level ∝;
p-value ( 0.0428 ) is less than significance level ∝ ( 0.05 )
so we reject Null Hypothesis H₀.
There is significant difference in the average amount of ice-cream that people scoop when a larger bowl is given to them.
Thus, Bowl size changes the selected portion size.
Explanation:
Given the data in the question;
n₁ = 26 n₂ = 22
y₁ = 5.07 y₂ = 6.58
s₁ = 1.84 s₂ = 2.91
Null hypothesis H₀ : μ₁ = μ₂
Alternative hypothesis H₁ : μ₁ < μ₂
Test Statistics
t = [( y₂-y₁) - ( μ₂-u₁ ) ] / √[ ( s₁²/n₁ ) + ( s₂²/n²) ]
we substitute
t = [( 6.58 - 5.07 ) - ( 0 ) ] / √[ ( (1.84)²/ 26 ) + ( (2.91)²/ 22 ) ]
t = [ 1.51 ] / √[ ( 3.3856 / 26 ) + ( 8.4681 / 22 ) ]
t = [ 1.51 ] / √[ 0.1302 + 0.3849 ]
t = [ 1.51 ] / √[ 0.5151 ]
t = [ 1.51 ] / 0.7177
t = 2.10394 ≈ 2.104
Given that; df = 34.3132 ≈ 34
p-value = 2P(
> 2.104 )
p-value = 2(1 - P(
< 2.104 ) ) { from table }
p-value = 2(1 - 0.9786 )
p-value = 2( 0.0214 )
p-value = 0.0428
AT 0.05 significance level ∝;
p-value ( 0.0428 ) is less than significance level ∝ ( 0.05 )
so we reject Null Hypothesis H₀.
There is significant difference in the average amount of ice-cream that people scoop when a larger bowl is given to them.
Thus, Bowl size changes the selected portion size.