A shoe company wants to compare two materials, A and B, for use on the soles of boys' shoes. In this example, each of ten boys in a study wore a special pair of shoes with the sole of one shoe made from Material A and the sole on the other shoe made from Material B. The sole types were randomly assigned to account for systematic differences in wear between the left and right foot. After three months, the shoes are measured for wear. Let Ho: μd = 0 versus Ha: μd ≠ 0. From this random sample of 10 boys, the sample mean difference was 0.41 and Sd was 0.387.
What is the value of the test statistic?
A) t = 0.00
B) t = 3.18
C) t = 3.35
D) t = 4.74
It is known that for right-handed people, the dominant (right) hand tends to be stronger. For left-handed people who live in a world designed for right-handed people, the same may not be true. To test this, muscle strength was measured on the right and left hands of a random sample of 15 left-handed men and the difference (left - right) was found. The alternative hypothesis is one-sided (left hand stronger). The resulting t-statistic was 1.90. Assuming the conditions are met, based on the t-statistic of 1.90 the appropriate decision for this test using α = 0.05 and using T-Table is:
A) df = 14, so p-value < 0.05 and the null hypothesis can be rejected.
B) df = 14, so p-value > 0.05 and the null hypothesis cannot be rejected.
C) df = 28, so p-value < 0.05 and the null hypothesis can be rejected.
D) df = 28, so p-value > 0.05 and the null hypothesis cannot be rejected.
A researcher wants to assess if there is a difference in the average age of onset of a certain disease for men and women who get the disease. Let μ1 = average age of onset for women and μ2 = average age of onset for men. A random sample of 30 women with the disease showed an average age of onset of 83 years, with a sample standard deviation of 11.5 years. A random sample of 20 men with the disease showed an average age of onset of 77 years, with a sample standard deviation of 4.5 years. Assume that ages at onset of this disease are normally distributed for each gender, do not assume the population variances are equal. What are the appropriate null and alternative hypotheses?
A) μ1 = μ2 and Ha: μ1 ≠ μ2
B) μ1 ≠ μ2 and Ha: μ1 = μ2
C) μ1 = μ2 and Ha: μ1 < μ2
D) μ1 = μ2 and Ha: μ1 > μ2