Unit 9 Prob and Stats Jeopardy

Sig Test Basics

Conditions

Testing a Claim for Proportions

Testing a Claim for Means

Movie Trivia

100

When do you reject the null hypothesis?

When the p-value is less than the alpha level

100

For the following problem, check the "random" condition ONLY

A recent report on elementary schools in Franklin county claimed that 13% of elementary students typically walk to school. Trey thinks that the proportion is less than 0.13 at his large elementary school (1000 students). Trey surveys a random sample of 80 students from his school and finds that 9 typically walk to school.

Random: Random sample of 80 students

100

Complete the STATE step only

An aspirin claims that 4 out of 5 doctors recommend its product. A consumer advocacy group believes the proportion is lower. To test the claim, a random sample of 50 doctors is selected, and 35 recommend this manufacturer's product. What would be the p-value?

p=the true proportion of doctors who recommend aspirin

H_o: p=0.8 (or 4/5)

H_a: p<0.8 (or 4/5)

alpha=0.05

100

Complete the STATE step only:

A manufacturer of high-performance lightbulbs claims that their new "LongLife" LED bulb has a mean lifespan of 8,000 hours. A consumer advocacy group suspects the actual mean lifespan is shorter than claimed.To test this, the group selects a random sample of 25 bulbs and finds a sample mean lifespan of 7,850 hours with a sample standard deviation 300 hours.

Is there enough evidence to support the claim that the true mean lifespan is less than 8,000 hours? Use alpha=0.1

H_o: μ = 8000

H_a: μ <8000

μ= the true mean lifespan of LongLife LED lightbulbs

alpha=0.1

100

In “The Lion King,” what is the name of Simba’s father?

Mufasa

200

If the alternative hypothesis for a problem is the following, what must the null hypothesis have been?

H_a: p<0.4

H_o: p=0.4

200

For the following problem, check the "Independent" condition ONLY

Independent: 80 is less than 10% of 1000 students

80 is less than 10% of the school

200

Complete the DO and CONCLUDE Step Only

A manufacturer of brick pavers maintains that 80% of the pavers produced by his company meet the standard 15-inch length. Of a random sample of 51 pavers 27 meet the standard. Does this show that the proportion of pavers that meet the standard is less than the manufacturer's claim, use α=0.05?

mean=0.8

st dev=sqrt(p_o(1-p_o)/n)=sqrt(.8*.2/51)=0.056

Normaldist(mean=0.8, stdev=0.056)

P(X≤ 27/51)=0

Since 0 is less than α=0.05, we reject H_o, we do have convincing evidence less than 80% of pavers meet the standard

200

A nutritionist claims that a new organic energy bar contains an average of 200 calories. A consumer group believes the bars actually contain more calories than advertised.

The group takes a random sample of 16 bars and finds a sample mean of 212 calories with a sample standard deviation of 24 calories.

Using a significance level of alpha = 0.05, determine if there is significant evidence to conclude that the mean calorie count is higher than the manufacturer’s claim.

mean=200

st dev=s_x/sqrt(n)=24/sqrt(16)=6

df=15

tdist(df=15, mean=200, stdev=6)

P(X≥ 212)=0.032

Since 0.032 is less than alpha=0.05, we reject H_o, we do have convincing evidence the bars have more than 200 calories on average

200

What is the subtitle of the upcoming Spiderman movie starring Tom Holland?

What is "Brand New Day"

300

For the following situation, describe a type I error and it's possible consequence:

The EPA believed that Volkswagon was cheating on car emissions tests. They tested a random sample of 500 Volkswagon diesel vehicles and found the probability their emissions were as claimed was 0.003, which was lower than their significance level of 0.05

A false positive: Volkwagon was not cheating and the random sample was just unlucky. A possible consequence would be Volkswagon being unfairly fined, "good" cars being recalled, etc.

300

For the following problem, check the NORMAL condition ONLY

A company claims that its new model of rechargeable batteries has a mean life of 500 charge cycles. A consumer protection group suspects the actual mean life is lower than claimed. They randomly select 50 batteries and test them until they fail. The sample results are:

Sample Mean=: 485 cycles

Sample Standard Deviation=30 cycles

Test the company's claim at a 0.05 significance level

Normal: n=50≥30 so ~Normal

300

Complete the DO and CONCLUDE steps only:

According to known data, 50% of women walk for exercise. We wonder if this is true for men. Of 75 randomly selected men, 32 walked for exercise. Is there evidence to show men are less likely to walk for exercise than women? Use alpha=0.05

mean=0.5

St dev=sqrt(p_o(1-p_o)/n)=sqrt(.5*.5/75)=0.058

normaldist(mean=0.5, st dev=0.058)

P(X ≤ 32/75)=0.103

With a p-value of .103≮ alpha=0.05, we fail to reject Ho. We do not have convincing evidence that less than 50% of men walk for exercise.

300

The mean ACT score of WJ students in 2010 was 20.6. the administration at WJ is concerned the ACT score is decreasing since COVID. They took a random sample of 30 student scores from 2021 to 2025 and found a mean of 19.9 with a standard deviation of 1.4. Does the administration have convincing evidence the true mean ACT score is lower than 20.6 since 2021? Use alpha 0.05

mean=20.6

st error=s_x/sqrt(n)=1.4/sqrt(30)=0.26

df=29

tdist(df=29,mean=20.6,st error=0.26)

P(X≤ 19.9)=0.006

Since 0.006 is less than 0.05, we reject Ho, we do have convincing evidence the average ACT score after 2020 is less than 20.6

300

What is ‘the Kragle’ in The Lego Movie?

What is Krazy Glue/Super Glue

400

For the following situation, describe a type II error and it's possible consequence:

The EPA believed that Volkswagon was cheating on car emissions tests. They tested a random sample of 500 Volkswagon diesel vehicles and found the probability their emissions were as claimed was 0.07, which was lower than their significance level of 0.05

A false negative, The EPA thinking Volkswagon isn't cheating on their emissions tests and they are. A possible consequence would be "bad" cars staying on the road, and Volkswagon continuing to cheat on emissions tests, leading to more environmental impacts, worse air conditions, etc.

400

For the following problem, check the "Normal" condition ONLY

A recent report on elementary schools in Madison county claimed that 13% of elementary students typically walk to school. Trey thinks that the proportion is less than 0.13 at his large elementary school (1000 students). Trey surveys a random sample of 80 students from his school and finds that 9 typically walk to school.

Normal: np_o=0.13*80=10.4≥10 and

n(1-po)=0.87*80=69.4≥10 so ~Normal

400

Complete the DO and CONCLUDE step only

mean=0.8

St dev=sqrt((p_o(1-p_o)/n)=sqrt((.8*.2)/50)=0.057

Normaldist(mean=0.8, st dev=0.057)

P(X≤35/50)=0.04

Since the p-value of 0.04 is less than alpha=0.05, we reject Ho. We do have convincing evidence that less than 4/5 of doctors recommend using aspirin

400

Complete the DO and CONCLUDE step only:

Is there enough evidence to support the claim that the true mean lifespan is less than 8,000 hours? Use alpha=0.1

mean=8000

st error=s_x/sqrt(n)=300/sqrt(25)=60

df=24

tdist(df=24,mean=8000,st error=60)

P(X≤ 7850)=0.01

Since 0.01 is less than 0.1, we reject Ho, we do have convincing evidence the average lifespan is less than 8000 hours

400

Which film is the famous line ‘Wax on, wax off’ from?

What is The Karate Kid?

500

How is the normal check different between confidence intervals for p and significance tests for p?

in CI you use p-hat*n and (1-p-hat)*n and compare each to 10

In Significance tests, you use the (H_o value)*n and (1-H_o value)*n and compare each to 10

500

Complete the PLAN step only

1-sample z-test for P

random: SRS of 50 doctors

Normal:

np_o=0.8*50=40≥10 and

n(1-po)=0.2*50=10≥10 so ~Normal

Independent: sampled less than 10% of doctors

500

Complete the DO and CONCLUDE steps only:

The poverty rate for the entire state is 8.9%. A random sample of adults is taken in a rural county. Of the 120 adults sampled, 16 live in poverty. Is there convincing statistical evidence to show that the poverty rate of this county is higher than that of the state? Use alpha=0.05

Mean=0.089

St dev=sqrt(p_o(1-p_o)/n)=sqrt(.089*.911/120)=0.026

Normaldist(mean=0.089, stdev=0.026)

P(X ≥ 16/120)=0.044

Since p=0.044<alpha=0.05, we reject Ho. There is convincing evidence that the poverty rate of this county is higher than that of the state.

500

A pharmaceutical company produces tablets that are supposed to contain exactly 500 mg of an active ingredient. The quality control team wants to ensure the machinery is calibrated correctly. If the mean is significantly higher or lower than 500 mg, the production line must be stopped.

They take a random sample of 30 tablets and find a sample mean=497 mg with a sample standard deviation=8 mg.

Using a significance level of alpha = 0.1, is there sufficient evidence to conclude that the mean amount of the active ingredient differs from the target 500 mg?

mean=500

st error=s_x/sqrt(n)=8/sqrt(30)=1.46

tdist(df=29,mean=500,st error=1.46)

P(X ≤ 497)=0.025

double since H_a is ≠ : 0.025*2=0.05

Since 0.05 is less than 0.1, we reject H_o, we do have convincing evidence that the mean active ingredient is not 500 mg.

500

In what movie does a character do the "Truffle Shuffle"?

What is The Goonies?