It has been claimed that 10.4% of adults who celebrate Halloween get inspiration

Question

It has been claimed that 10.4% of adults who celebrate Halloween get inspiration for Halloween costumes from Instagram. You believe this claimed value is on the low side and the true population parameter is larger than this claimed value. You survey a random sample of 325 adults who plan to celebrate Halloween, and you find that 46 of them reported getting costume inspiration from Instagram.

1. Suppose that rather than set up a one-sided (or one-tailed) alternative hypothesis, you had set up a two-sided (or two-tailed) alterative hypothesis because you were not sure if the sample results would be greater than or less than the claimed population value. Would your p-value have changed if you had done this? Please explain.

Explanation / Answer

H0: P = 0.104

H1: P > 0.104

p = 46/325 = 0.14

Standard deviation = sqrt (P * (1 - P)/n)

= sqrt (0.14 * 0.86/325)

= 0.019

The test statistic Z = (p - P)/SD

= (0.14 - 0.104)/0.019

= 1.89

P-value = P(Z > 1.89)

= 1 - P(Z < 1.89)

= 1 - 0.9706

= 0.0294

1) for two-sided

P-value = 2 * P(Z > 1.89)

= 2 * (1 - P(Z < 1.89))

= 2 * (1 - 0.9706)

= 2 * 0.0294

= 0.0588

Yes the p-value will be changed if we will take two-sided alternative hypothesis instead of one-sided hypothesis.

For two-sided alternative hypothesis the p-value will be greater than the p-value of one-sided alternative hypothesis.

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