Question

Share the null and alternative hypotheses for a decision that is relevant to your life. This can be a personal item or something at work. Define the population parameter, the appropriate test statistic formula, and if it is a one- or two-tailed test. Be sure to set up your hypotheses, too.

The two population parameters that we cover this week are:

μ: the population mean

and

p: the population proportion

Be sure to include numerical values for your variables. Additionally, identify the Type I and Type II Errors that could occur with your decision‐making process.

Answer 1

For my Friday movie night, what I really want to know is if one movie is significantly better than the others. In this case, I can build my hypothesis on the difference between the average rating my friends gave to each movie.

H0: µ_A =µ_B  v/s HA: µ_A ≠ µ_B

Which you can read as Null Hypothesis (H0): The mean of movie A is equal to the mean of movie B and Alternative Hypothesis (H1): The mean of movie A is not equal to the mean of movie B.

Here, we can use the t-test for difference of means.

P: the population proportion(I am giving a numerical example and decision about hypothesis).

Null hypothesis: P = 0.80

Alternative hypothesis: P ≠ 0.80

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.

• σ = sqrt[ P * ( 1 - P ) / n ]

  σ = sqrt [(0.8 * 0.2) / 100]

  σ = sqrt(0.0016) = 0.04

  z = (p - P) / σ = (.73 - .80)/0.04 = -1.75

  where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

  Since we have a two-tailed test, the P-value is the probability that the Z-score is less than -1.75 or greater than 1.75.

  We use the Normal Distribution Calculator to find P(z < -1.75) = 0.04, and P(z > 1.75) = 0.04. Thus, the P-value = 0.04 + 0.04 = 0.08​​ conclusion: Since the P-value (0.08) is greater than the significance level (0.05), we cannot reject the null hypothesis.