I. A penny was spun on a hard, flat surface 70 times. The outcomes are summarize

ID: 3326407 • Letter: I

Question

I. A penny was spun on a hard, flat surface 70 times. The outcomes are summarized in the following table. Using a Chi-Square test for goodness-of-fit, test the hypothesis that the coin is not fair, using a 0.05 level of significance. Outcomes Heads Tails Observed Counts 42 Expected Counts (a) State the null and alternative hypotheses. (4 points) (b) Compute the Chi-Square test statistic (Round 2 to 3 decimal places) (4 points) (c) Find the p-value. (4 points) (d) Make the conclusion. Do we have sufficient evidence to support that the penny is biased? (3 points)

Explanation / Answer

Part a

Here, we have to use Chi square test for goodness of fit. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: The coin is not fair.

Alternative hypothesis: Ha: The coin is fair.

We are given = 0.05

Part b

The test statistic formula is given as below:

Test statistic = Chi square = [(O – E)^2/E]

Calculation table for this test statistic is given as below:

Outcomes

Heads

Tails

Total

Observed Counts (O)

Expected Counts (E)

(O - E)

-7

(O - E)^2

(O - E)^2/E

1.4

2.8

Test statistic = Chi square = [(O – E)^2/E] = 2.800

Number of categories = N = 2

Degrees of freedom = N – 1 = 2 – 1 = 1

Part c

The P-value is given as 0.094264.

(By using Chi square table or excel)

Part d

P-value = 0.094264

= 0.05

P-value > = 0.05

So, we do not reject the null hypothesis that the coin is not fair.

There is insufficient evidence to conclude that the coin is fair.