Math / Data & Statistics

Question $\mu=23$ $\mu>32$ $\mu<352$ $\mu \neq 10$ a) Which statement could be used for the alternative hypothesis for a left-tail test? b) Which statement could be used for the null hypothesis? c) Which statement could be used for the alternative hypothesis for a two-tail test? d) Which statement could be used for the alternative hypothesis for a right-tail test?

Studdy Solution

STEP 1

What is this asking? We need to figure out which of these mathematical statements could be used as the null or alternative hypothesis in different types of hypothesis tests. Watch out! Don't mix up the null and alternative hypotheses!
The null hypothesis is what we're trying to disprove, and the alternative is what we suspect is true if the null is wrong.
Also, pay close attention to the direction of the inequality signs, they tell us whether it's a left-tailed, right-tailed, or two-tailed test!

STEP 2

1. Left-tail test
2. Null hypothesis
3. Two-tail test
4. Right-tail test

STEP 3

A left-tailed test looks for evidence that the population parameter is less than a specific value.
So, we're looking for an inequality with a less-than sign.

STEP 4

The statement $\mu < 352$ uses a less-than sign.
This means we're checking if the population mean, $\mu$ , is less than 352.
This fits the description of a left-tailed test perfectly!

STEP 5

The null hypothesis usually states that the population parameter is equal to a specific value.
It's the status quo, what we assume is true unless we have strong evidence against it.

STEP 6

The statement $\mu = 23$ uses an equals sign.
This says the population mean, $\mu$ , is equal to 23.
This is perfect for a null hypothesis!

STEP 7

A two-tailed test looks for evidence that the population parameter is not equal to a specific value.
It could be either greater than or less than the value, we're open to both possibilities.

STEP 8

The statement $\mu \neq 10$ uses a not-equal-to sign.
This means we're checking if the population mean, $\mu$ , is different from 10, either larger or smaller.
This is exactly what we want for a two-tailed test!

STEP 9

A right-tailed test looks for evidence that the population parameter is greater than a specific value.
We're looking for an inequality with a greater-than sign.

STEP 10

The statement $\mu > 32$ uses a greater-than sign.
This means we're checking if the population mean, $\mu$ , is greater than 32.
This is exactly what we're looking for in a right-tailed test!

STEP 11

a) Left-tail test: $\mu < 352$ b) Null hypothesis: $\mu = 23$ c) Two-tail test: $\mu \neq 10$ d) Right-tail test: $\mu > 32$

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Studdy Solution

STEP 1

STEP 2

1. Left-tail test
2. Null hypothesis
3. Two-tail test
4. Right-tail test

STEP 3

A left-tailed test looks for evidence that the population parameter is less than a specific value.
So, we're looking for an inequality with a less-than sign.

STEP 4

The statement $\mu < 352$ uses a less-than sign.
This means we're checking if the population mean, $\mu$ , is less than 352.
This fits the description of a left-tailed test perfectly!

STEP 5

The null hypothesis usually states that the population parameter is equal to a specific value.
It's the status quo, what we assume is true unless we have strong evidence against it.

STEP 6

The statement $\mu = 23$ uses an equals sign.
This says the population mean, $\mu$ , is equal to 23.
This is perfect for a null hypothesis!

STEP 7

A two-tailed test looks for evidence that the population parameter is not equal to a specific value.
It could be either greater than or less than the value, we're open to both possibilities.

STEP 8

The statement $\mu \neq 10$ uses a not-equal-to sign.
This means we're checking if the population mean, $\mu$ , is different from 10, either larger or smaller.
This is exactly what we want for a two-tailed test!

STEP 9

A right-tailed test looks for evidence that the population parameter is greater than a specific value.
We're looking for an inequality with a greater-than sign.

STEP 10

The statement $\mu > 32$ uses a greater-than sign.
This means we're checking if the population mean, $\mu$ , is greater than 32.
This is exactly what we're looking for in a right-tailed test!

STEP 11

a) Left-tail test: $\mu < 352$ b) Null hypothesis: $\mu = 23$ c) Two-tail test: $\mu \neq 10$ d) Right-tail test: $\mu > 32$

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Studdy Solution

STEP 1

STEP 2

1. Left-tail test2. Null hypothesis3. Two-tail test4. Right-tail test

STEP 3

A left-tailed test looks for evidence that the population parameter is *less than* a specific value.So, we're looking for an inequality with a less-than sign.

STEP 4

The statement μ<352\mu < 352μ<352 uses a less-than sign.This means we're checking if the population mean, μ\muμ, is less than **352**.This fits the description of a left-tailed test perfectly!

STEP 5

The null hypothesis usually states that the population parameter is *equal* to a specific value.It's the status quo, what we assume is true unless we have strong evidence against it.

STEP 6

The statement μ=23\mu = 23μ=23 uses an equals sign.This says the population mean, μ\muμ, is equal to **23**.This is perfect for a null hypothesis!

STEP 7

A two-tailed test looks for evidence that the population parameter is *not equal* to a specific value.It could be either greater than or less than the value, we're open to both possibilities.

STEP 8

The statement μ≠10\mu \neq 10μ=10 uses a not-equal-to sign.This means we're checking if the population mean, μ\muμ, is different from **10**, either larger or smaller.This is exactly what we want for a two-tailed test!

STEP 9

A right-tailed test looks for evidence that the population parameter is *greater than* a specific value.We're looking for an inequality with a greater-than sign.

STEP 10

The statement μ>32\mu > 32μ>32 uses a greater-than sign.This means we're checking if the population mean, μ\muμ, is greater than **32**.This is exactly what we're looking for in a right-tailed test!

STEP 11

a) Left-tail test: μ<352\mu < 352μ<352 b) Null hypothesis: μ=23\mu = 23μ=23 c) Two-tail test: μ≠10\mu \neq 10μ=10 d) Right-tail test: μ>32\mu > 32μ>32

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1. Left-tail test
2. Null hypothesis
3. Two-tail test
4. Right-tail test

A left-tailed test looks for evidence that the population parameter is less than a specific value.
So, we're looking for an inequality with a less-than sign.

The statement $\mu < 352$ uses a less-than sign.
This means we're checking if the population mean, $\mu$ , is less than 352.
This fits the description of a left-tailed test perfectly!

The null hypothesis usually states that the population parameter is equal to a specific value.
It's the status quo, what we assume is true unless we have strong evidence against it.

The statement $\mu = 23$ uses an equals sign.
This says the population mean, $\mu$ , is equal to 23.
This is perfect for a null hypothesis!

A two-tailed test looks for evidence that the population parameter is not equal to a specific value.
It could be either greater than or less than the value, we're open to both possibilities.

The statement $\mu \neq 10$ uses a not-equal-to sign.
This means we're checking if the population mean, $\mu$ , is different from 10, either larger or smaller.
This is exactly what we want for a two-tailed test!

A right-tailed test looks for evidence that the population parameter is greater than a specific value.
We're looking for an inequality with a greater-than sign.

The statement $\mu > 32$ uses a greater-than sign.
This means we're checking if the population mean, $\mu$ , is greater than 32.
This is exactly what we're looking for in a right-tailed test!

a) Left-tail test: $\mu < 352$ b) Null hypothesis: $\mu = 23$ c) Two-tail test: $\mu \neq 10$ d) Right-tail test: $\mu > 32$