Share
Explore BrainMass

# Hypothesis Testing - One- and Two-Tailed

Please see the attached file for the questions on weight-watching and chocolate bar taste.

#### Solution Preview

Instructions: For each statistical analysis, provide a response for the problem that includes your decision and your explanation of the decision. (The output is provided; you do not need to run the data.) You should include references to the statistical concepts and output in explaining why you made your decision. Answer all parts of the question. Please put your answer after the text question.

One Sample Hypothesis Testing (1 points)

1. A new weight-watching company, Weight Reducers International, advertises that those who join will lose, on the average, 10 pounds the first two weeks with a standard deviation of 2.8 pounds. A competitor is suspicious of the claim. A random sample of 50 people who joined the new weight reduction program revealed the mean loss to be 9 pounds. At the .05 level of significance, can we conclude that those joining Weight Reducers on average will lose less than 10 pounds? (Answer here)

Null Hypothesis : Those joining weight reducers will lose weight on average 10 pounds
or more.

(1) The reported p-value of Z is 0.0058 for this one tail test.
Since the reported p-value of 0.0058 is less than our designated significance level of
0.05, therefore we reject the hypothesis of mean loss of weight being equal to
10 pounds.
Thus we conclude at 0.05 significance level that those joining weight reducers
will lose on average less than 10 pounds.

(2) The reported calculated Z value is - 2.53.
The critical value of Z for 0.05 significance level is - 1.645 ( for left tail test).
Since the computed critical value of - 2.53 is less than the critical value of - 1.645
We conclude that the average loss of weight was less than 10 pounds at weight
reducers.

Hypothesis Test: Mean vs. Hypothesized Value

10.00 hypothesized value
9.00 mean labe
2.80 std. dev.
0.40 std. error
50 n

-2.53 z
.0058 p-value (one-tailed, lower)

Two Sample Tests of Hypothesis (1 point)

2. The following data resulted from a taste test of two different chocolate bars. The first number is a rating of the taste, which could range from 0 to 5, with a 5 indicating the person liked the taste. The second number indicates whether a "secret ingredient" was present. If the ingredient was present a code of 1 was used and a 0 otherwise. Assume the population standard deviations are the same. (a) At the .05 significance level, do these data show a difference in the taste ratings? (b) What test is used; is this an independent or paired sample? (c) Is this a one-tailed or two-tailed test? (Answer here)