Question

A taste test is done to see whether a person can tell Soda X from Soda Y. In each case, 38 random and independent trials are done (half with Soda X and half with Soda Y) in which the person determines whether she or he is drinking Soda X or Soda Y. One person gets 25 right out of 38 trials. Which graph shown below is the correct figure to test the hypothesis that the person can tell the difference? Explain your choice.

( A)

A graphing calculator output displays a coordinate system with horizontal axis from more than 3 ticks to the left of the vertical axis to more than 3 ticks to the right and a vertical axis from more than 1 tick below to 5 ticks above the horizontal axis. A Normal curve extends between the left and right edges of the graph with a peak 4 ticks high on the vertical axis at horizontal coordinate 0. Between the first and second tick marks to the right of the verical axis, a vertical line segment extends from the horizontal axis to the curve. The area under the curve to the right of the segment is shaded.

A graphing calculator output displays a coordinate system with horizontal axis from more than 3 ticks to the left of the vertical axis to more than 3 ticks to the right and a vertical axis from more than 1 tick below to 5 ticks above the horizontal axis. A Normal curve extends between the left and right edges of the graph with a peak 4 ticks high on the vertical axis at horizontal coordinate 0. Vertical line segments extend from the horizontal axis to the curve between the first and second tick marks to the left of the vertical axis and between the first and second tick marks to the right of the vertical axis. The areas under the curve to the left of the left segment and to the right of the right segment are shaded.

1-PropZTest z equals

1.9467

p equals 0.0258

1-PropZTest z equals

1.9467

p equals

0.0516

Graph

?

A

B

is the correct figure because the alternative hypothesis should be

?

two dash sided;

one dash sided;a person that can tell the difference between the sodas would have a

?

different result from

better result than

if they were simply guessing.

Answer 1

A taste test is done to see whether a person can tell Soda X from Soda Y. In each case, 38 random and independent trials are done (half with Soda X and half with Soda Y) in which the person determines whether she or he is drinking Soda X or Soda Y. One person gets 25 right out of 38 trials. Which graph shown below is the correct figure to test the hypothesis that the person can tell the difference? Explain your choice.

( A)

A graphing calculator output displays a coordinate system with horizontal axis from more than 3 ticks to the left of the vertical axis to more than 3 ticks to the right and a vertical axis from more than 1 tick below to 5 ticks above the horizontal axis. A Normal curve extends between the left and right edges of the graph with a peak 4 ticks high on the vertical axis at horizontal coordinate 0. Between the first and second tick marks to the right of the verical axis, a vertical line segment extends from the horizontal axis to the curve. The area under the curve to the right of the segment is shaded.

A graphing calculator output displays a coordinate system with horizontal axis from more than 3 ticks to the left of the vertical axis to more than 3 ticks to the right and a vertical axis from more than 1 tick below to 5 ticks above the horizontal axis. A Normal curve extends between the left and right edges of the graph with a peak 4 ticks high on the vertical axis at horizontal coordinate 0. Vertical line segments extend from the horizontal axis to the curve between the first and second tick marks to the left of the vertical axis and between the first and second tick marks to the right of the vertical axis. The areas under the curve to the left of the left segment and to the right of the right segment are shaded.

1-PropZTest z equals

1.9467

p equals

0.0516

Graph

B is the correct figure because the alternative hypothesis should be

two sided; a person that can tell the difference between the sodas would have a

different result from if they were simply guessing.

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis            p =	0.5
Level of Significance	0.05
Number of Items of Interest	25
Sample Size	38
Intermediate Calculations
Sample Proportion	0.657894737
Standard Error	0.0811
Z Test Statistic	1.9467
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.0516
Do not reject the null hypothesis