Question

1) The value of the z-score that is obtained for a hypothesis test is influenced by several factors. Some factors influence the size of the numerator of the z-score and other factors influence the size of the standard error in the denominator. For each of the following, indicate whether the factor influences the numerator or denominator of the z-score and determine whether the effect would be to increase the value of z (farther from zero) or decrease the value of z (closer to zero). In each case, assume that all other components of the z-score remain constant. (think of this as the A level question)

            a) Increase the sample size.

When sample size is increase, the standard error is reduced with a larger z-score(farther from zero) value.

            b) Increase the population standard deviation

when the population standard deviation is increase, the standard error is increased with smaller z-score (father from zero) value

c) Increase the difference between the sample mean and the value of m specified in the null hypothesis.

The null hypothesis states that there is no significant difference between the sample mean and the value of m

2) What are the four steps to hypothesis testing?

Step 1: State the hypotheses.

Step 2: Set the criteria for a decision.

Step 3: Compute the test statistic.

Step 4: Make a decision.

3) Suppose the time it takes to recognize common words like red and green is normally distributed with a m = 220 milliseconds and a s = 32. A psychologist presents a sample of n = 16 subjects with words that include names of colors. However, the color names are printed in a different color ink. That is, the word red might be printed in blue ink, or green might be printed in red. For these words, the sample had a mean reaction time of M = 240. Does presentation of color names in another color of ink alter reaction time? Alpha = .05       Follow the four steps from question 2… be sure to show each step.

4) People tend to evaluate the quality of their lives relative to others around them. To demonstrate this, researchers conducted interviews with twenty-five (25) frail elderly people. In the interview, each person was compared with fictitious others who were worse off (downward social comparison). After the interviews, the elderly people reported their level of satisfaction with their lives. The scores are measures on a life-satisfaction scale which has a mean of 20 and standard deviation of 4. The 25 elderly had a mean score of 21.65. Can we conclude that the people in the sample are significantly more satisfied than others in the general population? Test this with an alpha level of .05. (again, follow the 4 steps and state the conclusion in the context of the story)

Answer 1

1)

a. When the sample size (n) is increased the denominator i.e. decreases and the value of z increases (further from zero).

b. When the population standard deviation () increases the denominator i.e. increases and the value of z decreases (closer to zero).

c. Increase in the difference between the sample mean and the value of m specified in the null hypothesis will increase the numerator i.e. X(sample mean)-M(specified in null hypothesis) and the value of z increases (further from zero).

Please upload the questions separately.

Do comment for queries and leave a positive remark

X-M

(u) 0

We were unable to transcribe this image

(u) 0