Please show the work When engaging in weight control (fitness/fat burning) types
ID: 3156038 • Letter: P
Question
Please show the work
When engaging in weight control (fitness/fat burning) types of exercise, a person is expected to attain about 60% of their maximum heart rate. For 20-year-olds, this rate is approximately 120 bpm. A simple random sample of 100 20-year-olds was taken, and the sample mean was found to be 107 bpm with a standard deviation of 45 bpm. Researchers wonder if this is evidence to conclude that the expected level is actually lower than 120 bpm. To determine this, we test the following hypotheses:
H0 : m = 120, Ha : m < 120
3. The P-value for the one-sample t test is
a. larger than 0.10.
b. between 0.10 and 0.05.
c. between 0.05 and 0.01.
d. below 0.01.
4. Suppose the mean and standard deviation obtained were based on a sample of size 25 rather than 100. The P-value would be
a. larger.
b. smaller.
c. unchanged because the difference between and the hypothesized value m = 120 is unchanged.
d. unchanged because the variability measured by the standard deviation stays the same.
Explanation / Answer
3.
Formulating the null and alternative hypotheses,
Ho: u >= 120
Ha: u < 120
As we can see, this is a left tailed test.
df = n - 1 = 99
Getting the test statistic, as
X = sample mean = 107
uo = hypothesized mean = 120
n = sample size = 100
s = standard deviation = 45
Thus, t = (X - uo) * sqrt(n) / s = -2.888888889
Also, the p value is, using table,
OPTION D: BELOW 0.01 [ANSWER]
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4.
In that case, the t value will be smaller, so the P value will be
OPTION A: LARGER [ANSWER]