At the .10 level of significance, is the coin biased toward heads?

Question

A coin was flipped 60 times and came up heads 38 times. (a) At the .10 level of significance, is the coin biased toward heads? Show your decision rule and calculations. (b) Calculate a p-value and interpret it.

Answer 1

(a) ANSWER: Coin is biased toward "HEADS"

(b) ANSWER:  P-value ≤ α/2 (significance level) [0.0179  Ã¢Â‰Â¤  0.10/2]

Why???

POPULATION PROPORTION HYPOTHESIS TESTING, NORMAL DISTRIBUTION, "TWO-TAILED",  7-StepProcedure

1. PARAMETER OF INTEREST: p = POPULATION PROPORTION OF "HEADS"

2. HYPOTHESES : NULL HYPOTHESIS H0: p = 0.50 (50% - unbiased coin toward "HEADS")

ALTERNATIVE HYPOTHESIS H1: p ≠ 0.50 (NOT EQUAL to 50% - biased coin toward "HEADS")

3. COMPUTATION OF POPULATION PARAMETER: STANDARD DEVIATION

σ = sqrt[ p * ( 1 - p) / n ]

n = sample size [60]

σ = sqrt [0.50 * (1 - 0.50)/60] = (approx) 0.06455

4. COMPUTATION OF TEST STATISTIC ("critical value of z")

z = (p_hat - p) / σ

p_hat = SAMPLE PROPORTION [0.633] (38/60 of "HEADS")

z = (0.633-0.50)/  =  0.06455 = (approx.) 2.1

Valid when both conditions true:

n * p > 10 [60 *0.50 = 30 > 10] TRUE

n (1 − p) > 10 [60 * (1 - 0.5) = 30 > 10] TRUE

5. "P-value" "Look-up" value of Normal Distribution "area under the curve" "to the right" of z = 2.1 is (approx) 0.0179  the  "P-value"

6. TEST of P-value for "TWO-TAILED" level of significance. α/2 shows HALF in EACH TAIL.

P-value ≤ α/2 (significance level) [0.0179  Ã¢Â‰Â¤  0.10/2]; NULL HYPOTHESIS should be rejected.  Coin is biased toward "HEADS".

"When P-value is low, let it go" (let go the NULL HYPOTHESIS) P-value ≤ α

"When P-value is high, let it fly" (let fly the NULL HYPOTHESIS) P-value > α

7. CONCLUSION:

For signficance level α = 0.10, NULL HYPOTHESIS H0: p = 0.50 (50% - unbiased coin toward "HEADS") should be rejected. Coin is biased toward "HEADS".