Calculate the least squares regression line and write the equation.

Test the null hypothesis that the slope is zero (e.g., β=0).

Do College Students With Part-Time Jobs Sleep Less? College students were surveyed about the number of hours they sleep each night.Group A = With part-time jobs | Group B = Without jobs Group A: 6, 5, 7, 6, 5Group B: 8, 7, 9, 8, 7 Instructions: State your hypothesis and perform a two-sample t-test with all formulas. Create histograms for each group. Label axes and add titles. Comment on the distribution shape (e.g., normal, skewed, etc.).Solve on pen and paper

H0: mean egg weight is the same in all three diets HA: there is at least one difference among the means

This is advanced mathematics question that need detailed solutions

Question: Let F be a field. Prove that F contains a unique smallest subfield, called the prime subfield, which is isomorphic to either Q or Zp for some prime p. Instructions: • Begin by identifying the identity element 1 € F. • Use the closure under addition and inverses to build a subring. • • • Show that either the map ZF or Q →F is an embedding. Prove minimality and uniqueness. Discuss the characteristic of a field and link it to the structure of the prime subfield.

Topic: Group Theory | Abstract Algebra Question: Let G be a finite group of order 45. Prove that G has a normal subgroup of order 5 or order 9, and describe the number of Sylow subgroups for each. Instructions: • Use Sylow's Theorems (existence, conjugacy, and counting). • List divisors of 45 and compute possibilities for n for p = 3 and p = 5. Show that if n = 1, the subgroup is normal. Conclude about group structure using your analysis.

Topic: Group Theory | Abstract Algebra Question: Let G be a finite group of order 45. Prove that G has a normal subgroup of order 5 or order 9, and describe the number of Sylow subgroups for each. Instructions: • Use Sylow's Theorems (existence, conjugacy, and counting). • List divisors of 45 and compute possibilities for n for p = 3 and p = 5. Show that if n = 1, the subgroup is normal. Conclude about group structure using your analysis.

Topic: Group Theory | Abstract Algebra Question: Let G be a finite group of order 45. Prove that G has a normal subgroup of order 5 or order 9, and describe the number of Sylow subgroups for each. Instructions: • Use Sylow's Theorems (existence, conjugacy, and counting). • List divisors of 45 and compute possibilities for n for p = 3 and p = 5. Show that if n = 1, the subgroup is normal. Conclude about group structure using your analysis.