Question 1

The mean score for all NBA games during a particular season was less than 92 points per game. Write the null
and alternative hypotheses.

Accepted Answer

$\mathrm { H } _ { 0 } : \mu \geq 92 , \mathrm { H } _ { \mathrm { a } } : \mu < 92$

Question 2

A researcher claims that 71% of voters favor gun control. Determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed.
A)two-tailed
B)left-tailed
C)right-tailed

Accepted Answer

A two-tailed test is used when we are interested in determining whether a parameter is either greater than or less than a certain value (in this case, 71%). Since the claim does not specify a direction (only that the percentage is exactly 71%), we test for the possibility of the actual percentage being either higher or lower than this value.

Question 3

The mean score for all NBA games during a particular season was less than 106 points per game. State this
claim mathematically. Write the null and alternative hypotheses. Identify which hypothesis is the claim.

Accepted Answer

claim: $$\mu < 106 ; H _ { 0 } : \mu \geq 106 , H _ { a } : \mu < 106 \text {; claim is } H _ { a }$$

Question 4

A candidate for governor of a particular state claims to be favored by at least half of the voters. State this claim
mathematically. Write the null and alternative hypotheses. Identify which hypothesis is the claim.

Accepted Answer

The answer of A candidate for governor of a particular...

Question 5

The statement represents a claim. Write its complement and state which is $$\mathrm { H } _ { 0 }$$ and which is $\mathrm { H } _ { \mathrm { A } }$ $\mu$ = 8.3
A) $\mathrm { H } _ { 0 } : \mu = 8.3 \text { (claim); } \mathrm { H } _ { \mathrm { a } } : \mu \neq 8.3$
B) $\mathrm { H } _ { 0 } : \mu \neq 8.3 ; \mathrm { H } _ { \mathrm { a } } : \mu = 8.3 \text { (claim) }$
C) $\mathrm { H } _ { 0 } : \mu \geq 8.3 \text { (claim); } \mathrm { H } _ { \mathrm { a } } : \mu < 8.3$
D) $\mathrm { H } _ { 0 } : \mu \leq 8.3 ; \mathrm { H } _ { \mathrm { a } } : \mu > 8.3 \text { (claim) }$

Accepted Answer

The null hypothesis ($H_0$) is a statement of no effect or no difference and is the complement of the alternative hypothesis ($H_A$). Since the claim is $\mu = 8.3$, the null hypothesis is $H_0 : \mu = 8.3$, and its complement, the alternative hypothesis, is $H_A : \mu \neq 8.3$.

Question 6

The mean IQ of statistics teachers is greater than 160. Write the null and alternative hypotheses.

Accepted Answer

The answer of The mean IQ of statistics teachers is...

Question 7

The dean of a major university claims that the mean time for students to earn a Masterʹs degree is at most 3.3
years. Write the null and alternative hypotheses.

Accepted Answer

The answer of The dean of a major university claims...

Question 8

Given $\mathrm { H } _ { 0 } : \mathrm { p } \geq 80 \% \text { and } \mathrm { H } _ { \mathrm { a } } : \mathrm { p } < 80 \%$ determinedetermin whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
A)left-tailed
B)right-tailed
C)two-tailed

Accepted Answer

The alternative hypothesis ($H_a$) is $p < 80\%$, which suggests that the test is looking for evidence that the proportion is less than a certain value. This indicates a left-tailed test, as we are interested in the lower (left) end of the distribution.

Question 9

The alternative hypothesis is given with its graph. State the null hypothesis and sketch its graph. $\mathrm { H } _ { \mathrm { a } } : \mu < 9$ 
A) $\mathrm { H } _ { 0 } : \mu \geq 9$

B) $\mathrm { H } _ { 0 } : \mu \geq 9$

C) $\mathrm { H } _ { 0 } : \mu \leq 9$

D) $\mathrm { H } _ { 0 } : \mu > 9$

Accepted Answer

The answer of The alternative hypothesis is given with its...

Question 10

The mean IQ of statistics teachers is greater than 140. State this claim mathematically. Write the null and
alternative hypotheses. Identify which hypothesis is the claim.

Accepted Answer

The answer of The mean IQ of statistics teachers is...

Question 11

The mean age of bus drivers in Chicago is 56.9 years. State this claim mathematically. Write the null and
alternative hypotheses. Identify which hypothesis is the claim.

Accepted Answer

The answer of The mean age of bus drivers in...

Question 12

The alternative hypothesis is given with its graph. State the null hypothesis and sketch its graph. $\mathrm { H } _ { \mathrm { a } } : \mu \neq 5$ 
A) $\mathrm { H } _ { 0 } : \mu = 5$

B) $\mathrm { H } _ { 0 } : \mu \geq 5$

C) $\mathrm { H } _ { 0 } : \mu \leq 5$

D) $\mathrm { H } _ { 0 } : \mu > 5$

Accepted Answer

The answer of The alternative hypothesis is given with its...

Question 13

The dean of a major university claims that the mean time for students to earn a Masterʹs degree is at most 4.2
years. State this claim mathematically. Write the null and alternative hypotheses. Identify which hypothesis is
the claim.

Accepted Answer

The answer of The dean of a major university claims...

Question 14

The buyer of a local hiking club store recommends against buying the new digital altimeters because they vary
more than the old altimeters, which had a standard deviation of one yard. Write the null and alternative
hypotheses.

Accepted Answer

The answer of The buyer of a local hiking club...

Question 15

The mean age of bus drivers in Chicago is 48.6 years. Write the null and alternative hypotheses.

Accepted Answer

The answer of The mean age of bus drivers in...

Question 16

The buyer of a local hiking club store recommends against buying the new digital altimeters because they vary
more than the old altimeters, which had a standard deviation of one yard. State this claim mathematically.
Write the null and alternative hypotheses. Identify which hypothesis is the claim.

Accepted Answer

The answer of The buyer of a local hiking club...

Question 17

The statement represents a claim. Write its complement and state which is $\mathrm { H } _ { 0 }$ and which is $\mathrm { H } _ { \mathrm { A } }$ $p \leq$ .93
A) $\mathrm { H } _ { 0 } : \mathrm { p } \leq 0.93 \text { (claim); } \mathrm { H } _ { \mathrm { a } } : \mathrm { p } > 0.93$
B) $\mathrm { H } _ { 0 } : \mathrm { p } > 0.93 ; \mathrm { H } _ { \mathrm { a } } : \mathrm { p } \leq 0.93 \text { (claim) }$
C) $\mathrm { H } _ { 0 } : \mathrm { p } = 0.93 ; \mathrm { H } _ { \mathrm { a } } : \mathrm { p } \neq 0.93 \text { (claim) }$
D) $\mathrm { H } _ { 0 } : \mathrm { p } \geq 0.93 \text { (claim); } \mathrm { H } _ { \mathrm { a } } : \mathrm { p } < 0.93$

Accepted Answer

The null hypothesis ($H_0$) is typically a statement of no effect or no difference and is the complement to the alternative hypothesis ($H_A$). Since the claim is $p \leq .93$, the complement (alternative hypothesis) is $p > .93$, making choice A correct with $H_0: p \leq 0.93$ and $H_A: p > 0.93$.

Question 18

A candidate for governor of a particular state claims to be favored by at least half of the voters. Write the null
and alternative hypotheses.

Accepted Answer

The answer of A candidate for governor of a particular...

Question 19

Given $\mathrm { H } _ { 0 } : \mu \leq 25 \text { and } \mathrm { H } _ { \mathrm { a } } : \mu > 25 \text {, }$ determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
A)right-tailed
B)left-tailed
C)two-tailed

Accepted Answer

The alternative hypothesis ($H_a$) indicates the direction of the test. Since $H_a: \mu > 25$, it suggests that we are looking for values greater than 25, which means the test is right-tailed.

Question 20

The statement represents a claim. Write its complement and state which is $\mathrm { H } _ { 0 }$ and which is $\mathrm { H } _ { \mathrm { A } }$ $\sigma < 8.2$
A) $\mathrm { H } _ { 0 } : \sigma \geq 8.2 ; \mathrm { H } _ { \mathrm { a } } : \sigma < 8.2 \text { (claim) }$
B) $\mathrm { H } _ { 0 } : \sigma < 8.2 \text { (claim); } \mathrm { H } _ { \mathrm { a } } : \sigma \geq 8.2$
C) $\mathrm { H } _ { 0 } : \sigma \leq 8.2 \text { (claim); } \mathrm { H } _ { \mathrm { a } } : \sigma > 8.2$
D) $\mathrm { H } _ { 0 } : \sigma = 8.2 ; \mathrm { H } _ { \mathrm { a } } : \sigma \neq 8.2 \text { (claim) }$

Accepted Answer

The null hypothesis ($H_0$) is typically a statement of no effect or no difference and is the complement of the alternative hypothesis ($H_A$). Since the claim is $\sigma < 8.2$, the complement (and thus $H_0$) is $\sigma \geq 8.2$, making the claim the alternative hypothesis ($H_A$).

Quiz 7: Hypothesis Testing With One Sample

The mean score for all NBA games during a particular season was less than 92 points per game. Write the null and alternative hypotheses.

A researcher claims that 71% of voters favor gun control. Determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed.

The mean score for all NBA games during a particular season was less than 106 points per game. State this claim mathematically. Write the null and alternative hypotheses. Identify which hypothesis is the claim.

A candidate for governor of a particular state claims to be favored by at least half of the voters. State this claim mathematically. Write the null and alternative hypotheses. Identify which hypothesis is the claim.

The statement represents a claim. Write its complement and state which is $\mathrm { H } _ { 0 }$ and which is $\mathrm { H } _ { \mathrm { A } }$ $\mu$ = 8.3

The mean IQ of statistics teachers is greater than 160. Write the null and alternative hypotheses.

The dean of a major university claims that the mean time for students to earn a Masterʹs degree is at most 3.3 years. Write the null and alternative hypotheses.

Given $\mathrm { H } _ { 0 } : \mathrm { p } \geq 80 \% \text { and } \mathrm { H } _ { \mathrm { a } } : \mathrm { p } < 80 \%$ determinedetermin whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

The mean IQ of statistics teachers is greater than 140. State this claim mathematically. Write the null and alternative hypotheses. Identify which hypothesis is the claim.

The mean age of bus drivers in Chicago is 56.9 years. State this claim mathematically. Write the null and alternative hypotheses. Identify which hypothesis is the claim.

The dean of a major university claims that the mean time for students to earn a Masterʹs degree is at most 4.2 years. State this claim mathematically. Write the null and alternative hypotheses. Identify which hypothesis is the claim.

The buyer of a local hiking club store recommends against buying the new digital altimeters because they vary more than the old altimeters, which had a standard deviation of one yard. Write the null and alternative hypotheses.

The mean age of bus drivers in Chicago is 48.6 years. Write the null and alternative hypotheses.

The buyer of a local hiking club store recommends against buying the new digital altimeters because they vary more than the old altimeters, which had a standard deviation of one yard. State this claim mathematically. Write the null and alternative hypotheses. Identify which hypothesis is the claim.

The statement represents a claim. Write its complement and state which is $\mathrm { H } _ { 0 }$ and which is $\mathrm { H } _ { \mathrm { A } }$ $p \leq$ .93

A candidate for governor of a particular state claims to be favored by at least half of the voters. Write the null and alternative hypotheses.

Given $\mathrm { H } _ { 0 } : \mu \leq 25 \text { and } \mathrm { H } _ { \mathrm { a } } : \mu > 25 \text {, }$ determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

The statement represents a claim. Write its complement and state which is $\mathrm { H } _ { 0 }$ and which is $\mathrm { H } _ { \mathrm { A } }$ $\sigma < 8.2$

Quiz 7: Hypothesis Testing With One Sample

The mean score for all NBA games during a particular season was less than 92 points per game. Write the null and alternative hypotheses.

A researcher claims that 71% of voters favor gun control. Determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed.

The mean score for all NBA games during a particular season was less than 106 points per game. State this claim mathematically. Write the null and alternative hypotheses. Identify which hypothesis is the claim.

A candidate for governor of a particular state claims to be favored by at least half of the voters. State this claim mathematically. Write the null and alternative hypotheses. Identify which hypothesis is the claim.

The statement represents a claim. Write its complement and state which is H0\mathrm { H } _ { 0 }H0​ and which is HA\mathrm { H } _ { \mathrm { A } }HA​ μ\muμ = 8.3

The mean IQ of statistics teachers is greater than 160. Write the null and alternative hypotheses.

The dean of a major university claims that the mean time for students to earn a Masterʹs degree is at most 3.3 years. Write the null and alternative hypotheses.

Given H0:p≥80% and Ha:p<80%\mathrm { H } _ { 0 } : \mathrm { p } \geq 80 \% \text { and } \mathrm { H } _ { \mathrm { a } } : \mathrm { p } < 80 \%H0​:p≥80% and Ha​:p<80% determinedetermin whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

The alternative hypothesis is given with its graph. State the null hypothesis and sketch its graph. Ha:μ<9\mathrm { H } _ { \mathrm { a } } : \mu < 9Ha​:μ<9

The mean IQ of statistics teachers is greater than 140. State this claim mathematically. Write the null and alternative hypotheses. Identify which hypothesis is the claim.

The mean age of bus drivers in Chicago is 56.9 years. State this claim mathematically. Write the null and alternative hypotheses. Identify which hypothesis is the claim.

The alternative hypothesis is given with its graph. State the null hypothesis and sketch its graph. Ha:μ≠5\mathrm { H } _ { \mathrm { a } } : \mu \neq 5Ha​:μ=5

The dean of a major university claims that the mean time for students to earn a Masterʹs degree is at most 4.2 years. State this claim mathematically. Write the null and alternative hypotheses. Identify which hypothesis is the claim.

The buyer of a local hiking club store recommends against buying the new digital altimeters because they vary more than the old altimeters, which had a standard deviation of one yard. Write the null and alternative hypotheses.

The mean age of bus drivers in Chicago is 48.6 years. Write the null and alternative hypotheses.

The buyer of a local hiking club store recommends against buying the new digital altimeters because they vary more than the old altimeters, which had a standard deviation of one yard. State this claim mathematically. Write the null and alternative hypotheses. Identify which hypothesis is the claim.

The statement represents a claim. Write its complement and state which is H0\mathrm { H } _ { 0 }H0​ and which is HA\mathrm { H } _ { \mathrm { A } }HA​ p≤p \leqp≤ .93

A candidate for governor of a particular state claims to be favored by at least half of the voters. Write the null and alternative hypotheses.

Given H0:μ≤25 and Ha:μ>25, \mathrm { H } _ { 0 } : \mu \leq 25 \text { and } \mathrm { H } _ { \mathrm { a } } : \mu > 25 \text {, }H0​:μ≤25 and Ha​:μ>25, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

The statement represents a claim. Write its complement and state which is H0\mathrm { H } _ { 0 }H0​ and which is HA\mathrm { H } _ { \mathrm { A } }HA​ σ<8.2\sigma < 8.2σ<8.2

The statement represents a claim. Write its complement and state which is $\mathrm { H } _ { 0 }$ and which is $\mathrm { H } _ { \mathrm { A } }$ $\mu$ = 8.3

Given $\mathrm { H } _ { 0 } : \mathrm { p } \geq 80 \% \text { and } \mathrm { H } _ { \mathrm { a } } : \mathrm { p } < 80 \%$ determinedetermin whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

The statement represents a claim. Write its complement and state which is $\mathrm { H } _ { 0 }$ and which is $\mathrm { H } _ { \mathrm { A } }$ $p \leq$ .93

Given $\mathrm { H } _ { 0 } : \mu \leq 25 \text { and } \mathrm { H } _ { \mathrm { a } } : \mu > 25 \text {, }$ determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

The statement represents a claim. Write its complement and state which is $\mathrm { H } _ { 0 }$ and which is $\mathrm { H } _ { \mathrm { A } }$ $\sigma < 8.2$