Math 1342
HW 7 (Fall 2022)
1) The mean age of students at one CCQ statistic class is 24 years. Write the null and alternative
hypotheses.
2) A college claims that the mean time for students to earn an associate degree is at most 5 semesters.
Write the null and alternative hypotheses.
3) A car maker claims that one of its cars gets better than 20 Km per liter. Determine whether the
hypothesis test for this is left-tailed, right-tailed, or two-tailed.
4) Given Ho:
80% and Ha:
< 80%, determine whether the hypothesis test is left-tailed,
right-tailed, or two-tailed.
5) The mean age of students at one college is 23 years. If a hypothesis test is performed, how should
you interpret a decision that fails to reject the null hypothesis?
A) There is not sufficient evidence to reject the claim µ = 23.
B) There is sufficient evidence to reject the claim µ = 23.
C) There is not sufficient evidence to support the claim µ = 23.
D) There is sufficient evidence to support the claim µ = 23.
6) Suppose you want to test the claim that
significance of
< 65.4. Given a sample size of n = 35 and a level of
= 0.05, when should you reject H o?
A) Reject Ho if the standardized test statistic is less than -1.28.
B) Reject Ho if the standardized test statistic is less than -1.645.
C) Reject Ho if the standardized test is less than -1.96.
D) Reject Ho if the standardized test statistic is less than -2.33.
7) The P-value for a hypothesis test is P = 0.034. Do you reject or fail to reject H 0 for level of
significance
= 0.05
8) Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to
reject H 0 for the level of significance .
Two-tailed test, z = -1.63,
= 0.05
9) Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to
reject Ho for the level of significance .
Left-tailed test,
z = -1.83,
10) Find the standardized test statistic t for a sample with n = 15, x = 7.2, s = 0.8, and
Ho:
= 0.05
= 0.05, if
6.9.
11) Find the critical value and rejection region for the type of z-test with level of significance .
Left-tailed test,
= 0.05
12) Find the critical value and rejection region for the type of t-test with level of significance
sample size n.
Right-tailed test,
and
= 0.1, n = 35
13) Find the critical value and rejection region for the type of z-test with level of significance .
Two-tailed test,
= 0.10
14) A fast food outlet claims that the mean waiting time in line is less than 3.8 minutes. A random
sample of 60 customers has a mean of 3.7 minutes with a population standard deviation of 0.6
minute. If = 0.05, test the fast food outlet's claim. (Use the P-Value Method)
a) State the hypotheses, and Identify the claim.
b) Find the standardized test statistic z.
c) Find the P-value.
d) Decide whether to reject the null hypothesis or not.
e) Interpret the decision in the context of the original claim.
15) A researcher claims that the mean age of residents in a small city is more than 21 years. A random
sample of 37 residents has a mean age of 19 years with a standard deviation of 4 years. If
is there enough evidence to reject the researcher's claim?
= 0.01,
a) Identify the claim and state the hypothesis
b) Find the critical value and identify the rejection region.
c) Find the standardized test statistic z. Sketch a graph.
d) Decide whether to reject the null hypothesis.
e) Interpret the decision in the context of the original claim.
16) A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1400 hours. A homeowner
selects 25 bulbs and finds the mean lifetime to be 1390 hours with a standard deviation of 80 hours.
Test the manufacturer's claim. Use = 0.05.
a) Identify the claim and state the hypothesis
b) Find the critical value and identify the rejection region.
c) Find the standardized test statistic t. Sketch a graph.
d) Decide whether to reject the null hypothesis.
e) Interpret the decision in the context of the original claim.
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