Math / Data & Statistics

Question2. At significance level $\alpha=0.10$ , determine if the mull hy pothesis should be rejected given the test statistic and p-value. Interpret the result. a. The FDA mandates that the average number of rodent hairs in a sumple of apple butter be no more than 4 hairs. A consumer advocacy group claims that a cerrain brand is violating this standard. The test statistic is found to be 294 and the p-value is 0.0016. b. A report states that doctors are late for $12 \%$ of all appointments. A doctor claims that less than $12 \%$ of his appointments are taken late. The test statistic is found to be -0.44 and the p -value is 0.3299 . c. A company claims it has redesigned light bulbs to last longer. The previous design had an average life of 1200 hours. The test statistic is 2.08 and the $p$ -value is 0.0188

Studdy Solution

STEP 1

1. We are using a significance level of $\alpha = 0.10$ .
2. The null hypothesis ( $H_0$ ) is assumed to be true unless evidence suggests otherwise.
3. The decision to reject the null hypothesis is based on the comparison of the p-value to the significance level.

STEP 2

1. Compare the p-value to the significance level for each scenario.
2. Determine whether to reject the null hypothesis.
3. Interpret the result.

STEP 3

For scenario (a), compare the p-value $0.0016$ to $\alpha = 0.10$ .
$0.0016 < 0.10$

STEP 4

Since $0.0016 < 0.10$ , reject the null hypothesis for scenario (a).

STEP 5

Interpretation for scenario (a): There is sufficient evidence at the $\alpha = 0.10$ level to support the consumer advocacy group's claim that the brand is violating the FDA standard.

STEP 6

For scenario (b), compare the p-value $0.3299$ to $\alpha = 0.10$ .
$0.3299 > 0.10$

STEP 7

Since $0.3299 > 0.10$ , do not reject the null hypothesis for scenario (b).

STEP 8

Interpretation for scenario (b): There is not sufficient evidence at the $\alpha = 0.10$ level to support the doctor's claim that less than $12\%$ of his appointments are late.

STEP 9

For scenario (c), compare the p-value $0.0188$ to $\alpha = 0.10$ .
$0.0188 < 0.10$

STEP 10

Since $0.0188 < 0.10$ , reject the null hypothesis for scenario (c).

STEP 11

Interpretation for scenario (c): There is sufficient evidence at the $\alpha = 0.10$ level to support the company's claim that the redesigned light bulbs last longer than the previous design.

Was this helpful?

Studdy Solution

STEP 1

1. We are using a significance level of $\alpha = 0.10$ .
2. The null hypothesis ( $H_0$ ) is assumed to be true unless evidence suggests otherwise.
3. The decision to reject the null hypothesis is based on the comparison of the p-value to the significance level.

STEP 2

1. Compare the p-value to the significance level for each scenario.
2. Determine whether to reject the null hypothesis.
3. Interpret the result.

STEP 3

For scenario (a), compare the p-value $0.0016$ to $\alpha = 0.10$ .
$0.0016 < 0.10$

STEP 4

Since $0.0016 < 0.10$ , reject the null hypothesis for scenario (a).

STEP 5

Interpretation for scenario (a): There is sufficient evidence at the $\alpha = 0.10$ level to support the consumer advocacy group's claim that the brand is violating the FDA standard.

STEP 6

For scenario (b), compare the p-value $0.3299$ to $\alpha = 0.10$ .
$0.3299 > 0.10$

STEP 7

Since $0.3299 > 0.10$ , do not reject the null hypothesis for scenario (b).

STEP 8

Interpretation for scenario (b): There is not sufficient evidence at the $\alpha = 0.10$ level to support the doctor's claim that less than $12\%$ of his appointments are late.

STEP 9

For scenario (c), compare the p-value $0.0188$ to $\alpha = 0.10$ .
$0.0188 < 0.10$

STEP 10

Since $0.0188 < 0.10$ , reject the null hypothesis for scenario (c).

STEP 11

Interpretation for scenario (c): There is sufficient evidence at the $\alpha = 0.10$ level to support the company's claim that the redesigned light bulbs last longer than the previous design.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

1. We are using a significance level of α=0.10\alpha = 0.10α=0.10.2. The null hypothesis (H0H_0H0​) is assumed to be true unless evidence suggests otherwise.3. The decision to reject the null hypothesis is based on the comparison of the p-value to the significance level.

STEP 2

1. Compare the p-value to the significance level for each scenario.2. Determine whether to reject the null hypothesis.3. Interpret the result.

STEP 3

For scenario (a), compare the p-value 0.00160.00160.0016 to α=0.10\alpha = 0.10α=0.10.0.0016<0.10 0.0016 < 0.10 0.0016<0.10

STEP 4

Since 0.0016<0.100.0016 < 0.100.0016<0.10, reject the null hypothesis for scenario (a).

STEP 5

Interpretation for scenario (a): There is sufficient evidence at the α=0.10\alpha = 0.10α=0.10 level to support the consumer advocacy group's claim that the brand is violating the FDA standard.

STEP 6

For scenario (b), compare the p-value 0.32990.32990.3299 to α=0.10\alpha = 0.10α=0.10.0.3299>0.10 0.3299 > 0.10 0.3299>0.10

STEP 7

Since 0.3299>0.100.3299 > 0.100.3299>0.10, do not reject the null hypothesis for scenario (b).

STEP 8

Interpretation for scenario (b): There is not sufficient evidence at the α=0.10\alpha = 0.10α=0.10 level to support the doctor's claim that less than 12%12\%12% of his appointments are late.

STEP 9

For scenario (c), compare the p-value 0.01880.01880.0188 to α=0.10\alpha = 0.10α=0.10.0.0188<0.10 0.0188 < 0.10 0.0188<0.10

STEP 10

Since 0.0188<0.100.0188 < 0.100.0188<0.10, reject the null hypothesis for scenario (c).

STEP 11

Interpretation for scenario (c): There is sufficient evidence at the α=0.10\alpha = 0.10α=0.10 level to support the company's claim that the redesigned light bulbs last longer than the previous design.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. We are using a significance level of $\alpha = 0.10$ .
2. The null hypothesis ( $H_0$ ) is assumed to be true unless evidence suggests otherwise.
3. The decision to reject the null hypothesis is based on the comparison of the p-value to the significance level.

1. Compare the p-value to the significance level for each scenario.
2. Determine whether to reject the null hypothesis.
3. Interpret the result.

For scenario (a), compare the p-value $0.0016$ to $\alpha = 0.10$ .
$0.0016 < 0.10$

Since $0.0016 < 0.10$ , reject the null hypothesis for scenario (a).

Interpretation for scenario (a): There is sufficient evidence at the $\alpha = 0.10$ level to support the consumer advocacy group's claim that the brand is violating the FDA standard.

For scenario (b), compare the p-value $0.3299$ to $\alpha = 0.10$ .
$0.3299 > 0.10$

Since $0.3299 > 0.10$ , do not reject the null hypothesis for scenario (b).

Interpretation for scenario (b): There is not sufficient evidence at the $\alpha = 0.10$ level to support the doctor's claim that less than $12\%$ of his appointments are late.

For scenario (c), compare the p-value $0.0188$ to $\alpha = 0.10$ .
$0.0188 < 0.10$

Since $0.0188 < 0.10$ , reject the null hypothesis for scenario (c).

Interpretation for scenario (c): There is sufficient evidence at the $\alpha = 0.10$ level to support the company's claim that the redesigned light bulbs last longer than the previous design.