A cosmetics counter at Acadian Mall observed a difference in the sales between the male and female sale associates. A sample of 30 days revealed the women sold a mean of $1500 per day. A sample of 40 days revealed the men sold a mean of $1450 per day. Assume the population standard deviation for men is $150 and for women $100. At the 0.01 significance level, can the manager conclude that the mean amount sold per day for the men is different from that of the women? Question to address here: state the null and alternate hypothesis.
Added by Josefina M.
Step 1
- Null hypothesis: H0: μ_m = μ_w (the mean amount sold per day by men equals that by women) - Alternative hypothesis: H1: μ_m ≠ μ_w (the means are different) Show more…
Show all steps
Close
Your feedback will help us improve your experience
Shubham Sharma and 60 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Tom Sevits is the owner of the Appliance Patch. Recently, Tom observed a difference in the dollar value of sales between the men and women he employs as sales associates. A sample of 40 days revealed that the men sold a mean of $1400 worth of appliances per day. For a sample of 50 days, the women sold a mean of $1500 worth of appliances per day. Assume the population standard deviation for men is $200 and for women is $250. At the 0.05 significance level, can Mr. Sevits conclude that the mean amount sold per day is larger for the women? a) State the null hypothesis and the alternative hypothesis. b) What is the decision rule? c) What is the value of the test statistic? d) What is your decision regarding the null hypothesis? e) What is the p-value? f) Interpret the result.
Shubham S.
Tom Sevits is the owner of the Appliance Patch. Recently, Tom observed a difference in the dollar value of sales between the men and women he employs as sales associates. A sample of 40 days revealed that the men sold a mean of $1400 worth of appliances per day. For a sample of 50 days, the women sold a mean of $1500 worth of appliances per day. Assume the population standard deviation for men is $200 and for women is $250. At the 0.05 significance level, can Mr. Sevits conclude that the mean amount sold per day is larger for the women? a) State the null hypothesis and the alternative hypothesis. b) What is the decision rule? c) What is the value of the test statistic? d) What is your decision regarding the null hypothesis? e) What is the p-value? f) Interpret the result. a) Hypotheses: Null Hypothesis (H0): The mean amount sold per day is the same for men and women. Alternative Hypothesis (HA): The mean amount sold per day is larger for women than for men. b) Decision Rule: If the test statistic is greater than the critical value, reject the null hypothesis. Otherwise, do not reject the null hypothesis. c) Test Statistic Value: To determine the test statistic value, we need to calculate the z-score using the formula: z = (x1 - x2) / √((σ1^2 / n1) + (σ2^2 / n2)) where x1 and x2 are the sample means, σ1 and σ2 are the population standard deviations, and n1 and n2 are the sample sizes. d) Decision regarding the null hypothesis: Based on the test statistic value and the decision rule, we will either reject or fail to reject the null hypothesis. e) P-value: The p-value is the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true. f) Result Interpretation: Based on the p-value, we can determine whether there is sufficient evidence to suggest that the mean amount sold per day is larger for women.
Ivan K.
Tom Sevits is the owner of the Appliance Patch. Recently Tom observed a difference in the dollar value of sales between the men and women he employs as sales associates. A sample of 40 days revealed the men sold a mean of $1 ,400 worth of appliances per day with a standard deviation of $200. For a sample of 50 days, the women sold a mean of $1 ,500 worth of appliances per day with a standard deviation of $250. At the .05 significance level can Mr. Sevits conclude that the mean amount sold per day is larger for the women? (a) State the null hypothesis and the alternate hypothesis. (b) What is the decision rule? (c) What is the value of the test statistic? (d) What is your decision regarding the null hypothesis? (e) What is the p-value? (t) Interpret the result.
Vaidik S.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD