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.

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.

Step-by-step 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( [tex]t_{34[/tex] > 2.104 )

p-value = 2(1 - P( [tex]t_{34[/tex] < 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.