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15:07, 11/01/2026
STATS 202 - Exercise 2: Two Sample Hypothesis Testing Overview - Studocu STATS Exercises 8 Two Sample Hypothesis Testing
1. Test the hypothesis that the average SAT math scores from students in California
and New York are different. A sample of 45 students from California had an
average score of 552, whereas a sample of 38 New York students had an average
score of 530. Assume the population standard deviations for California and New
York students are 105 and 114 respectively. a. Test at the = 0.05 level.
b. Find the p-value for these samples.
2. A company tracks satisfaction scores based on customer feedback from individual
stores on a scale from 0 to 100. The following data represents the customer scores from Store 1 and Store 2. Store 1 : 90 87 93 75 88 96 90 82 95 97 78
sample mean = 88.3, sample standard deviation=7.30 Store 2: 82 85 90 74 80 89 75 81 93 75
sample mean = 82.4, sample standard deviation=6.74
Assume population standard deviations are equal but unknown and that the population is
normally distributed. Test the hypotheses H0: = vs. H1: ≠ H0: ≤ vs. H1: > H0: ≥ vs. H1: < using = 0.10, Where:
= the mean satisfaction scores of store 1.
= the mean satisfaction scores of store 2. 15:07, 11/01/2026
STATS 202 - Exercise 2: Two Sample Hypothesis Testing Overview - Studocu
3. Re-do question 2, but this time assume the population standard deviations are unequal and unknown. 15:07, 11/01/2026
STATS 202 - Exercise 2: Two Sample Hypothesis Testing Overview - Studocu
4. Bank of America’s Consumer Spending Survey collected data on annual credit card
charges in seven different categories of expenditures: transportation, groceries,
dining out, household expenses, home furnishings, apparel and entertainment. Using data from a sample of
accounts, assume that each account was
used to identify the annual credit card charges for and the
annual credit card charges for Using the difference data, 𝑑= $850 and the 𝑠 =$1,123
a. Formulate the null and alternative hypotheses to test for no difference
between the population mean credit card charges for groceries and the
population mean credit card charges for dining out.
b. Use a 0.05 level of significance. Can you conclude that the population means differ? c. What is the p-value?
d. Which category, groceries or dining out, has a higher population mean annual credit card charge?
5. Airline travelers often choose which airport to fly from based on flight cost. Cost
data (in dollars) for a sample of flights to , and
Louisville, Kentucky, were collected to help determine which of the two airports
was more costly to fly from. A researcher argued that it is significantly more to fly out o
lle. Use the sample data to see whether they
support the researcher’s argument, Use 𝛼 = 5% s the level of significance. Destination Dayton Louisville Chicago-O’Hare $319 $142 Grand Rapids, Michigan 192 213 Portland, Oregon 503 317 Atlanta, Georgia 256 387 Seattle, Washington 339 317 South Bend, Indiana 379 167 Miami, Florida 268 273 Dallas-Ft. Worth, Texas 288 274 15:07, 11/01/2026
STATS 202 - Exercise 2: Two Sample Hypothesis Testing Overview - Studocu 318 261,25 93,74 82,60 15:07, 11/01/2026
STATS 202 - Exercise 2: Two Sample Hypothesis Testing Overview - Studocu
6. In recent years, a growing array of entertainment options competes for consumer
time. By 2004, cable television and radio surpassed broadcast television, recorded
music, and the daily newspaper to become the two entertainment media with the
greatest usage. Researchers used a sample of 15 individuals and collected data on
the hours per week spent watching cable television and hours per week spent listening to radio. Individual Television Radio 1 22 25 2 8 10 3 25 29 4 22 19 5 12 13 6 26 28 7 22 23 8 19 21 9 21 21 10 23 23 11 14 15 12 14 18 13 14 17 14 16 15 15 24 23
a. Use a 0.05 level of significance and test for a difference between the population mean
usage for cable television and radio. b. What is the p-value?
c. What is the sample mean number of hours per week spent listening to radio?
d. Which medium has greater usage? 15:07, 11/01/2026
STATS 202 - Exercise 2: Two Sample Hypothesis Testing Overview - Studocu 15:07, 11/01/2026
STATS 202 - Exercise 2: Two Sample Hypothesis Testing Overview - Studocu