Question

A jar contains 4 blue buttons, 5 green buttons, and 1 white button. A student chooses a button, records its color, and then places the button back in the jar. The student repeats this process 50 times. The table shows the results. Color Frequency Blue26Green21White3 Questions Was each color chosen more or fewer times than expected? Select one choice from each set to complete the statements.Response area with 6 radio buttons within 3 groups.Blue was chosen ,begin bold,[more / fewer] ,end bold,times than expected. Green was chosen ,begin bold,[more / fewer],end bold, times than expected. White was chosen ,begin bold,[more / fewer] ,end bold,times than expected.

Answer 1

To determine if each color was chosen more or fewer times than expected, we first need to calculate the expected frequency for each color based on their proportions in the jar.

Total number of buttons = 4 (blue) + 5 (green) + 1 (white) = 10 buttons.

Expected probabilities:

• Probability of blue = 4/10 = 0.4
• Probability of green = 5/10 = 0.5
• Probability of white = 1/10 = 0.1

In 50 trials, the expected frequency for each color is:

• Expected frequency of blue = 50 * 0.4 = 20
• Expected frequency of green = 50 * 0.5 = 25
• Expected frequency of white = 50 * 0.1 = 5

Now we compare the expected frequencies with the observed frequencies (given in the question):

• Blue: Observed = 26, Expected = 20
• Green: Observed = 21, Expected = 25
• White: Observed = 3, Expected = 5

Now let's draw conclusions:

1. Blue was chosen more times than expected (26 vs 20).
2. Green was chosen fewer times than expected (21 vs 25).
3. White was chosen fewer times than expected (3 vs 5).

So the completed statements are:

• Blue was chosen more times than expected.
• Green was chosen fewer times than expected.
• White was chosen fewer times than expected.