Math / Data & Statistics

QuestionSubmit Answer
5. [-/12.5 Points] DETAILS MY NOTES BBUNDERSTAT13 8.1.021. How much a customer buys is a direct result of how much time they spend in a store. A study of average shopping times in a large chain store gave the following information: Shopping alone: 9 min. Shopping with a family: 31 min. Suppose you want to set up a statistical test to challenge the claim that people who shop alone spend, on average, 19 minutes shopping in a store. (a) What would you use for the null and alternate hypotheses (in min) if you believe the average shopping time is less than 19 minutes? (Enter != for as needed.) Ho H1 Is this a right-tailed, left-tailed, or two-tailed test? O right-tailed two-tailed left-tailed (b) What would you use for the null and alternate hypotheses (in min) if you believe the average shopping time is different from 19 minutes? (Enter != for as needed.) Ho₁ H₁i Is this a right-tailed, left-tailed, or two-tailed test? O right-tailed O two-tailed O left-tailed

Studdy Solution

STEP 1

What is this asking? We're trying to figure out if people shopping alone spend less time than 19 minutes or just a different amount of time than 19 minutes on average in a store. Watch out! Don't mix up the null and alternate hypotheses, and remember to choose the right type of test: right-tailed, left-tailed, or two-tailed!

STEP 2

1. Define the null and alternate hypotheses for part (a)
2. Determine the type of test for part (a)
3. Define the null and alternate hypotheses for part (b)
4. Determine the type of test for part (b)

STEP 3

Identify the claim: We believe the average shopping time is less than 19 minutes.

STEP 4

Set up the null hypothesis: The null hypothesis ( $H_0$ ) is the statement we assume to be true before testing.
Here, it would be that the average shopping time is 19 minutes.
So, we write: $H_0: \mu = 19$

STEP 5

Set up the alternate hypothesis: The alternate hypothesis ( $H_1$ ) is what we want to test against the null hypothesis.
Since we believe the time is less, we write: $H_1: \mu < 19$

STEP 6

Since the alternate hypothesis is testing if the average time is less than 19 minutes, this is a left-tailed test.

STEP 7

Identify the claim: We believe the average shopping time is different from 19 minutes.

STEP 8

Set up the null hypothesis: Again, the null hypothesis ( $H_0$ ) assumes the average shopping time is 19 minutes: $H_0: \mu = 19$

STEP 9

Set up the alternate hypothesis: Here, we want to test if the time is different, so we write: $H_1: \mu \neq 19$

STEP 10

Since the alternate hypothesis is testing if the average time is different from 19 minutes, this is a two-tailed test.

STEP 11

For part (a): - Null Hypothesis: $H_0: \mu = 19$ - Alternate Hypothesis: $H_1: \mu < 19$ - Type of Test: Left-tailed
For part (b): - Null Hypothesis: $H_0: \mu = 19$ - Alternate Hypothesis: $H_1: \mu \neq 19$ - Type of Test: Two-tailed

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Studdy Solution

STEP 1

STEP 2

1. Define the null and alternate hypotheses for part (a)
2. Determine the type of test for part (a)
3. Define the null and alternate hypotheses for part (b)
4. Determine the type of test for part (b)

STEP 3

Identify the claim: We believe the average shopping time is less than 19 minutes.

STEP 4

Set up the null hypothesis: The null hypothesis ( $H_0$ ) is the statement we assume to be true before testing.
Here, it would be that the average shopping time is 19 minutes.
So, we write: $H_0: \mu = 19$

STEP 5

Set up the alternate hypothesis: The alternate hypothesis ( $H_1$ ) is what we want to test against the null hypothesis.
Since we believe the time is less, we write: $H_1: \mu < 19$

STEP 6

Since the alternate hypothesis is testing if the average time is less than 19 minutes, this is a left-tailed test.

STEP 7

Identify the claim: We believe the average shopping time is different from 19 minutes.

STEP 8

Set up the null hypothesis: Again, the null hypothesis ( $H_0$ ) assumes the average shopping time is 19 minutes: $H_0: \mu = 19$

STEP 9

Set up the alternate hypothesis: Here, we want to test if the time is different, so we write: $H_1: \mu \neq 19$

STEP 10

Since the alternate hypothesis is testing if the average time is different from 19 minutes, this is a two-tailed test.

STEP 11

For part (a): - Null Hypothesis: $H_0: \mu = 19$ - Alternate Hypothesis: $H_1: \mu < 19$ - Type of Test: Left-tailed
For part (b): - Null Hypothesis: $H_0: \mu = 19$ - Alternate Hypothesis: $H_1: \mu \neq 19$ - Type of Test: Two-tailed

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Studdy Solution

STEP 1

STEP 2

1. Define the null and alternate hypotheses for part (a)2. Determine the type of test for part (a)3. Define the null and alternate hypotheses for part (b)4. Determine the type of test for part (b)

STEP 3

**Identify the claim**: We believe the average shopping time is less than **19 minutes**.

STEP 4

**Set up the null hypothesis**: The null hypothesis (H0H_0H0​) is the statement we assume to be true before testing.Here, it would be that the average shopping time is **19 minutes**.So, we write: H0:μ=19 H_0: \mu = 19 H0​:μ=19

STEP 5

**Set up the alternate hypothesis**: The alternate hypothesis (H1H_1H1​) is what we want to test against the null hypothesis.Since we believe the time is less, we write: H1:μ<19 H_1: \mu < 19 H1​:μ<19

STEP 6

Since the alternate hypothesis is testing if the average time is **less than 19 minutes**, this is a **left-tailed test**.

STEP 7

**Identify the claim**: We believe the average shopping time is different from **19 minutes**.

STEP 8

**Set up the null hypothesis**: Again, the null hypothesis (H0H_0H0​) assumes the average shopping time is **19 minutes**: H0:μ=19 H_0: \mu = 19 H0​:μ=19

STEP 9

**Set up the alternate hypothesis**: Here, we want to test if the time is different, so we write: H1:μ≠19 H_1: \mu \neq 19 H1​:μ=19

STEP 10

Since the alternate hypothesis is testing if the average time is **different from 19 minutes**, this is a **two-tailed test**.

STEP 11

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1. Define the null and alternate hypotheses for part (a)
2. Determine the type of test for part (a)
3. Define the null and alternate hypotheses for part (b)
4. Determine the type of test for part (b)

Identify the claim: We believe the average shopping time is less than 19 minutes.

Set up the null hypothesis: The null hypothesis ( $H_0$ ) is the statement we assume to be true before testing.
Here, it would be that the average shopping time is 19 minutes.
So, we write: $H_0: \mu = 19$

Set up the alternate hypothesis: The alternate hypothesis ( $H_1$ ) is what we want to test against the null hypothesis.
Since we believe the time is less, we write: $H_1: \mu < 19$

Since the alternate hypothesis is testing if the average time is less than 19 minutes, this is a left-tailed test.

Identify the claim: We believe the average shopping time is different from 19 minutes.

Set up the null hypothesis: Again, the null hypothesis ( $H_0$ ) assumes the average shopping time is 19 minutes: $H_0: \mu = 19$

Set up the alternate hypothesis: Here, we want to test if the time is different, so we write: $H_1: \mu \neq 19$

Since the alternate hypothesis is testing if the average time is different from 19 minutes, this is a two-tailed test.