Question

A) To test whether a coin is biased, we have these hypotheses: H0: p = 0.5, H1: p is not 0.5, where p is the population proportion of "heads" when the coin is tossed. A random sample of 50 tosses resulted in 30 heads. What is the value of the test statistic (Zstat) for this sample? (Provide two decimal places)

B) A sample data set consists of these values: 5, 2, 1, 5.

Find the z-score of 5. (Provide two digits after the decimal point)

Answer 1

Solution:-

A)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P = 0.80
Alternative hypothesis: P 0.80

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).

S.D = 0.070711
z = (p - P) /S.D

z = 1.41

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 -1.41 or greater than 1.41.

P-value = P(z < - 1.41) + P(z > 1.41)

Use z-calculator to find the p-values.

P-value = 0.0793 + 0.0793

Thus, the P-value = 0.1586

Interpret results. Since the P-value (0.1586) is greater than the significance level (0.05), we cannot reject the null hypothesis.

B)

Mean = 3.25

x = 5

By applying normal distribution:-

z = 1.6974