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MATH/STAT 203 A - Probability and Statistics I (SP 2025)

MATH/STAT 203 A - Probability and Statistics I (SP 2025)

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My patient was watching the news while she was in her hospital room. When I came in to see her and check her vital signs and medications, she asked: What does Dr. Henry mean with "the false negative rate of Covid-19 tests can be as high as 30%"? I explained to her that she means:

That 70% of those who get a positive are actually not infected.

That 70% of those who are infected will get a positive if they are tested.

That 30% of those who are no infected will get a negative if they are tested.

That 30% of those who get a negative are actually not infected.

That this is not important, just that fewer than 30% actually have Covid-19.

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Consider a weighted coin with 29% probability of landing heads.

If this coin is tossed 5 times, what is the probability of getting exactly 2 heads?

Enter your answer as a decimal number.

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In a test for one population mean, if the null hypothesis is rejected when the alternative hypothesis is true then:

a correct decision is made.

✅

a CI should be used instead of a test.

❌

a Type I error is made.

❌

a Type II error is made.

❌

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If the confidence level of a CI increases then the value of the multiplier

Stays the same

It's quadrupled

Increases

Decreases

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If you take random samples of the same size repeatedly from the same population, and for each sample you construct a 95% confidence interval for the population mean, then about 95% of the intervals should contain the sample mean.

The length of a pregnancy is normally distributed with mean 268 days and standard deviation 15 days. What is more likely to find?

25 women whose mean length of pregnancy is less than 273 days.

✅

25 women whose mean length of pregnancy is less than 253 days.

❌

A woman whose pregnancy is less than 253 days.

❌

A woman whose pregnancy is at least 273 days.

❌

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Identify the type of sampling that is used in the following scenario. -- In order to find out whether vaccinations depends on race a sample is collected as follows: four ethnic groups are selected at random and a sample from each is included in the study. --

Stratified

Simple

Systematic

Cluster

The anual income of single adults in Canada is normally distributed with a mean of $45,000 and a standard deviation of $10,000. It the z-score of the income of an individual is 3.5 then

her income is less than that of 99% of the population

her income is exceeded by 99% of the population

her income is in the bottom 1% of the distribution

her income is exceeded by less than 1% of the population

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We could use a -test to investigate

the relationship between gender and hair color

✅

the correlation between age and income

❌

the relationship between gender and income

❌