Question

Hypothesis Testing with One Population

The credit manager of a discount department store believes that the average age of his charge account customers is less than 40 years. A random sample of 100 charge account customers revealed an average age of 36 years and a standard deviation of 10 years. Do these data provide sufficient evidence to support the credit manager's belief? (Use 95% confidence)

Answer 1

Sample mean age = x^bar = 36 Sample standard deviation = s = 10 Sample size = n = 100 Significance level = alpha = 1 - 0.95 = 0.05 Degrees of Freedom = df = n - 1 = 100 - 1 = 99 H_0: mu greaterthanorequalto 40 H_1: mu < 40 Test Statistic: t = (x^bar - mu)/(s/squareroot n) t = 36 - 40/10/squareroot 100 t = -4.00 From t-distribution table: area under the curve to the left of (t = -4.00) and for (df = 99), is given by: 0.0001 Hence, p-value = 0.0001 Since p-value is less than the value, of (alpha = 0.05), we reject H_0 Conclusion: Hence, the data provide the sufficient evidence to support the credit manager's belief that the average age of his charge account customers is less than 40 years The p-value is greater than alpha Therefore, we cannot reject the null hypothesis. Final Conclusion: There is not sufficient