Understanding T-Tests and Conditions

Sunil and his friends use a messaging app and suspect they send over 100 messages daily. To test this, Sunil takes a random sample of seven days and calculates a mean of 125 messages with a standard deviation of 44. He plans to conduct a t-test to determine if the average is indeed over 100. The conditions for the test include randomness, independence, and normality. While the sample is random and independent, it does not meet the normal condition due to its small size and skewed distribution.

What is Sunil's suspicion about the average number of messages sent per day?

• Exactly 125 messages

• More than 100 messages

• Exactly 100 messages

• Less than 50 messages

What is the null hypothesis in Sunil's study?

• The mean number of messages is 100

• The mean number of messages is more than 125

• The mean number of messages is less than 100

• The mean number of messages is 125

What is the sample size used by Sunil for his analysis?

• 7 days

• 10 days

• 5 days

• 30 days

What is the purpose of conducting a significance test in this context?

• To calculate the standard deviation

• To determine the probability of the sample mean under the null hypothesis

• To estimate the sample mean

• To prove the null hypothesis

What is the random condition in a significance test?

• The sample must be symmetric

• The sample size must be greater than 30

• The sample must be random

• The sample must be taken from a normal distribution

How can independence be ensured in Sunil's sample?

• By having a sample size greater than 30

• By using a normal distribution

• By sampling with replacement

• By ensuring the sample is symmetric

What is the normal condition in the context of a t-test?

• The sampling distribution of the sample means should be approximately normal

• The sample size must be less than 10% of the population

• The sample must be random

• The sample must be taken with replacement

Why is the normal condition not met in Sunil's study?

• The sample size is too large

• The sample data is strongly skewed to the right

• The sample is not random

• The sample size is greater than 30

What is one way to feel confident about the normality of the sampling distribution?

• If the sample is taken with replacement

• If the sample is random

• If the sample is symmetric with no significant outliers

• If the sample size is less than 10% of the population

What is the standard deviation of the sample data in Sunil's study?

• 365 messages

• 44 messages

• 125 messages

• 100 messages