Sketch a standard normal curve

Reference no: EM132336051

Statistics One Proportion Z-Test Assignment -

Q1. In the past, the proportion of women in a certain population who were taller than 63 inches was 80%. A researcher believes that this proportion has increased. In a random sample of 200 women in this population, 170 of them are taller than 63 inches. Test the researcher's claim at the significance level α = 0.05.

(a) The null hypothesis is H₀: p = 0.80. (Here, p₀ = 0.80). Write the alternative hypothesis.

(b) Find p^{^} = x/n.

z = (p^{^} - P₀)/(√(p₀(1-p₀)/n))

(d) Sketch a standard normal curve, and shade the area that represents the P-value. Find the P-value using the normaldcf on your calculator.

(e) Compare the P-value with the significance level, α = 0.05, in order to make your decision. State your decision (reject the null hypothesis or fail to reject the null hypothesis).

(f) State your conclusion.

Q2. In 2001, 38% of families reported that their family regularly ate dinner together. A researcher believes that this proportion has decreased. In a recent poll, 35.9% of 1122 families reported that their family regularly ate dinner together. Use α = 0.05. You may use the 1-PropZTest on your graphing calculator.

(a) State the null and alternative hypotheses.

(b) This time p^{^} = 0.359 and n = 1122 are given to you. Find x = np^{^}. (You will need to round the result to the nearest whole number.)

(d) Give the P-value (round to 3 decimal places).

(e) State your decision.

(f) State your conclusion.

Q3. Test the hypotheses

H₀: p = 0.4

H₁: p ≠ 0.4

at the level α = 0.01. The sample data are n = 500, x = 220. You may use your graphing calculator.

(a) Give the sample proportion. p^{^} =

(b) Give the test statistic (round to 2 decimal places). z₀ =

(d) State your decision.

(e) Construct a 99% confidence interval for the population proportion.

(f) Does your confidence interval contain p₀ = 0.4? Does this confirm your decision in part (d)?

(g) Suppose that everything in the original problem remains the same except that the sample data are n = 5000, x = 2200. (The sample proportion is exactly the same as it was before!) Repeat the test, and report the new test statistic, the new P-value, and your new decision.

Instructions: Must use a scientific calculator where stated.

Reference no: EM132336051

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