Question

Hypothesis Testing

For 1-3 below simply set up the Null (Ho) and Alternative (H1) Hypothesis.

1/ Test the claim that less than 10% of households own a boat.

2/ Test the claim that the mean body weight of college students is greater than 160 lbs.

3/ Test the claim that the majority of people prefer iphones.

4/ For 4 and 5 below, perform the hypothesis test. (a) Set up the null and alternative hypothesis (b) Calculate the test statistic (c) Calculate the p-value (d) Reject or Fail to reject the Null (e) Make your conclusion.

5/ In a recent poll of 240 people, 67% indicated that the sale of firearms should be made stricter. Use a significance level of 0.05 to test the claim that the majority of people want stricter gun control laws.

6/ In a recent survey of 100 women, it was determined that the average age of marriage was 25 with a standard deviation of 3. Use a significance level of 0.05 to test the claim that the average of marriage for women is greater than 22 years of age (the average in 1980).

Answer #1

1)

H0 : p = 0.10

Ha : p < 0.10

2)

H0 : mu = 160

Ha : mu > 160

3)

5)

H0 : p = 0.5

Ha ; p > 0.5

Test statistics:

z = ( P - p) /sqrt(p*(1-p)/n)

= (0.67 - 0.5)/sqrt(0.5 * (1-0.5)/240)

= 5.2673

p value = 0.00001

we reject the null hypothesis

There is sufficient evidence to support the claim

6)

Hypothesis;

H0 : mu = 22

Ha : mu > 22

Test statistics:

z = ( x -mean)/(s/sqrt(n))

= ( 25 - 22)/(3/sqrt(100))

= 10

p value = 0.00001

we reject the null hypothesis

There is sufficient evidence to support the claim

Identify the null and alternative hypothesis(in symbolic and
sentence form), test statistic, P-value(or critical values),
conclusion about the null hypothesis, and final conclusion that
addresses the original claim (Don’t just say Reject the null
hypothesis or fail to reject the null hypothesis).
4. Test the claim that the mean age of the prison population in
one city is less than 26 years. Sample data are summarized as
n=25,x ̅=24.4,and s=9.2. Use a significance level of α=0.05.

From the table below: (1) Set up the Null and Alternative
hypothesis. (2) What Hypothesis should be rejected and what
resulted to that decision. (3) Using the values in the table, what
will be the P-value and t-Test Statistic if the population 1 sample
is changed to 20 and population 2 sample size is changed to 14.
Hypothesized Mean Difference
0
Level of significance
0.05
Population 1 Sample
Sample Size
18
Sample Mean
99210
Sample SD
13577
Population 2 Sample...

Determine whether the claim stated below represents the null
hypothesis or the alternative hypothesis. If a hypothesis test is
performed, how should you interpret a decision that (a) rejects
the null hypothesis or (b) fails to reject the null
hypothesis?
A scientist claims that the mean incubation period for the eggs of
a species of bird is less than 36 days.
Does the claim represent the null hypothesis or the alternative
hypothesis?
Since the claim
▼
a statement of equality,...

1. In testing a null hypothesis H0 versus an alternative Ha, H0
is ALWAYS rejected if
A. at least one sample observation falls in the non-rejection
region.
B. the test statistic value is less than the critical value.
C. p-value ≥ α where α is the level of significance. 1
D. p-value < α where α is the level of significance.
2. In testing a null hypothesis H0 : µ = 0 vs H0 : µ > 0,
suppose Z...

Determine whether the claim stated below represents the null
hypothesis or the alternative hypothesis. If a hypothesis test is
performed, how should you interpret a decision that (a) rejects
the null hypothesis or (b) fails to reject the null
hypothesis?
A researcher claims that the standard deviation of the life of a
certain type of lawn mower is less than 2.4 years
Does the claim represent the null hypothesis or the alternative
hypothesis?
Since the claim a) -------- a statement...

Identify the null and alternative hypothesis(in symbolic and
sentence form), test statistic, P-value(or critical values),
conclusion about the null hypothesis, and final conclusion that
addresses the original claim (Don’t just say Reject the null
hypothesis or fail to reject the null hypothesis).
2. According to a recent poll 53% of Americans would
vote for the incumbent president. If a random sample of 100 people
results in 45% who would vote for the incumbent, test the claim
that the actual percentage is...

Identify the null hypothesis, alternative hypothesis, test
statistic, P-value, conclusion about the null hypothesis, and final
conclusion that addresses the original claim. Test the claim that
the mean lifetime of car engines of a particular type is greater
than 220,000 miles. Sample data are summarized as n = 23, ?̅ =
226,450 miles, and s = 11,500 miles. Use a significance level of ?
= 0.01.

Determine whether the claim state
below represents the null hypothesis or the alternative hypothesis.
If a hypothesis test is performed, how should you interpret a
decision that A.) rejects the null or B.) fails to reject the null
hypothesis?
A scientist claims that the mean
incubation period for the eggs of a species of a bird is more than
51 days.
Does the claim represent the null
hypothesis or the alternative hypothesis?
Since the claim ____ a statement of
equality,...

Identify the null hypothesis, alternative hypothesis, test
statistic, P-value, conclusion about the null hypothesis, and final
conclusion that addresses the original claim. A survey of 1025
adults found that 113 of them, or 11%, said they or a household
member had been a victim of a computer or internet crime on their
home computer in the past year. At the 0.05 level of significance,
test the claim that the rate of internet crime victims is less than
12%.

Determine whether the claim stated below represents the null
hypothesis or the alternative hypothesis. If a hypothesis test is?
performed, how should you interpret a decision that? (a) rejects
the null hypothesis or? (b) fails to reject the null? hypothesis? A
scientist claims that the mean incubation period for the eggs of a
species of bird is less than 35 days.

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