You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. You sample 30 night students, and the sample mean GPA is 2.35 with a standard deviation of 0.46. You sample 25 day students, and the sample mean GPA is 2.58 with a standard deviation of 0.47. Test the claim using a 5% level of significance. Assume the sample standard deviations are unequal and that GPAs are normally distributed.

Hypotheses:

H₀: ₁= ₂

H₁: ₁₂

What is the p-value for this scenario? Round to four decimal places. Make sure you put the 0 in front of the decimal.

p-value =___

A new over-the-counter medicine to treat a sore throat is to be tested for effectiveness. The makers of the medicine take two random samples of 25 individuals showing symptoms of a sore throat. Group 1 receives the new medicine and Group 2 receives a placebo. After a few days on the medicine, each group is interviewed and asked how they would rate their comfort level 1-10 (1 being the most uncomfortable and 10 being no discomfort at all). The results are below. Find the 95% confidence interval in the difference of the mean comfort level. Is there sufficient evidence to conclude that the new medicine is effective? Assume the data is normally distributed with unequal variances. (Round answers to 4 decimal places) Make sure you put the 0 in front of the decimal.

Average Group 1 = 5.84, SD Group 1 = 2.211334, n1 = 25

Average Group 2 = 3.96, SD Group 2 = 2.35372, n2 = 25

___< ₁- ₂<___

___

You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. You sample 30 night students, and the sample mean GPA is 2.35 with a standard deviation of 0.46. You sample 25 day students, and the sample mean GPA is 2.58 with a standard deviation of 0.47. Test the claim using a 5% level of significance. Assume the sample standard deviations are unequal and that GPAs are normally distributed.

Hypotheses:

H₀: ₁(?)₂

H₁: ₁(?)₂

What are the correct hypotheses for this problem?

Question 13 options:

H₀: ₁= ₂; H₁: ₁>₂

H₀: ₁< ₂; H₁: ₁=₂

H₀: _{1 2}; H₁: ₁₂

H₀: _{1 2}; H₁: ₁₂

H₀: ₁= ₂; H₁:₁₂

H₀: _{1 2}; H₁: ₁=₂

In a survey of 1000 high school students in Oregon, the average SAT score for 500 students who chose to go out of state for college (Group 1) was 1225 and the average SAT score for 500 students who chose to stay in state for college (Group 2) was 1130. The population standard deviation for students who choose to go out of state is 95 and the population standard deviation for students who choose to stay in state is 103. Find a 95% confidence interval and decide if the SAT scores between the two groups is significantly different. Confidence Interval (round to 4 decimal places):

___< 1 - 2 <___

___

Question 14 options:

Blank # 1

Blank # 2

In a random sample of 50 Americans five years ago (Group 1), the average credit card debt was $5,779. In a random sample of 50 Americans in the present day (Group 2), the average credit card debt is $6,499, Let the population standard deviation be $1,152 five years ago, and let the current population standard deviation be $1,634. Using a 0.01 level of significance, test if there is a difference in credit card debt today versus five years ago. What is the p-value? Make sure you put the 0 in front of the decimal.

(Round to 4 decimal places) p-value =___

In a two-tailed 2-sample z-test you find a P-Value of 0.0278. At what level of significance would you choose to reject the null hypothesis? Select all that apply.

Question 16 options:

0.05

0.08

0.10

0.01

In a random sample of 50 Americans five years ago (Group 1), the average credit card debt was $5,798. In a random sample of 50 Americans in the present day (Group 2), the average credit card debt is $6,511. Let the population standard deviation be $1,154 five years ago, and let the current population standard deviation be $1,645. Using a 0.01 level of significance, test if there is a difference in credit card debt today versus five years ago.

What are the correct hypotheses for this problem?

Question 17 options:

H₀: ₁= ₂; H₁: ₁₂

H₀: _{1 2}; H₁: ₁₂

H₀: _{1 2}; H₁: ₁=₂

H₀: _{1 2}; H₁: ₁₂

H₀: ₁= ₂; H₁: ₁>₂

H₀: ₁< ₂; H₁: ₁=₂

The CDC national estimates that 1 in 68 = 0.0147 children are diagnosed with have been diagnosed with Autism Spectrum Disorder (ASD). A researcher believes that the proportion of children in their county is different from the CDC estimate.

The hypotheses are:

H₀:p= 0.0147

H₁:p 0.0147

What is a type II error in the context of this problem?

Question 18 options:

The proportion of children diagnosed with ASD in the researcher's county is believed to be different from the national estimate and the proportion is different.

The proportion of children diagnosed with ASD in the researcher's county is believed to be different from the national estimate, even though the proportion is the same.

The proportion of children diagnosed with ASD in the researcher's county is believed to be the same as the national estimate and the proportion is the same.

The proportion of children diagnosed with ASD in the researcher's county is believed to be the same as the national estimate, even though the proportion is the different.

Which of the following symbols represents power ?

Question 19 options:

(1-)*100%

1-

The average age of an adult's first vacation without a parent or guardian was reported to be 23 years old. A travel agent believes that the average age is different from reported. They sample 28 adults and they asked their age in years when they first vacationed as an adult without a parent or guardian, data shown below.

See Excel for Data.

adult vacation data.xlsx

Test the claim using a 10% level of significance.

The hypotheses for this problem are:

H₀: = 23

H₁: 23

Find the test statistic. Round answer to 4 decimal places. test statistic t =