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.

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.

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(   > 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.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

-6 is the correct option from the above given options