Final answer:
The question explores statistical methods to estimate sample mean and standard deviation, and conducts hypothesis testing to compare means and assess claims about population parameters using given sample data.
Step-by-step explanation:
The subject question deals with various statistical concepts pertaining to hypothesis testing, sample mean estimation, and standard deviation estimation. We will address the parts of the question sequentially to provide clarity on these topics.
Sample Mean and Standard Deviation
To estimate the sample mean money spent on Valentine's day, you would sum up all the individual amounts spent by the students and divide by the number of students. For the estimation of the sample standard deviation, we'd use the formula for standard deviation, which is the square root of the variance.
Hypothesis Testing
In hypothesis tests, such as comparing the mean expenditures on texts and supplies by university students, we'd typically start by proposing a null hypothesis (H0) that there is no difference between the means. Then we decide on an alternative hypothesis (HA) that suggests the means are different. We would conduct the test using a formula that incorporates the sample means, population standard deviations, and sample sizes.
Understanding Distributions
When testing for differences in study habits, we would likely use a t-distribution if the population standard deviation is unknown and the sample size is small. Since in the provided question the standard deviation is known and the sample size is small (less than 30), the z-distribution could be used.