QUESTIONS

  • (a) What are the steps involved in hypothesis testing? (b) How do you decide what the null hypothesis is and when would you reject a null hypothesis? (c) if you fail to reject the null hypothesis, what would be its implications? (5 pts.)

 

  • The average work week for Americans has been recorded as 43 hours nationally. A local leisure product marketer randomly selects 44 sales people and asks them to keep a log book of hours worked. Suppose the sample average turns out to be 40.5 hours with a standard deviation of 9 hours. Conduct a hypothesis testing for the claim that Americans are now working less (show all steps and use 95 % confidence). Discuss the potential business implications from your result (10 pts- 7 pts for hypothesis testing and 3 pts for business implications).

 

  • In 2014, the average number of years passenger cars were being used was 6.5 years. In 2015, a sample of 100 passenger cars showed a sample mean of 7.8 years and a sample standard deviation of 2.2 years. Use a .05 level of significance (p< .05) and test the claim that people use their cars for longer period of time. What marketing suggestions do you have for vehicle manufacturers? (10 pts- 7 pts for hypothesis testing and 3 pts for business implications).

 

  • Q-Mart is interested in comparing its male and female customers. Q-Mart would like to know if its female customers spend more money, on average, than its male customers.  They have collected random samples of 25 female customers and 22 male customers.  On average, women customers spend $102.23 with a sample standard deviation of 93.4 and men customers spend $86.46 with a sample standard deviation of 59.7.  Using a 10% level of significance, is there sufficient evidence for Q-Mart to conclude that women customers on average spend more than men customers?  Please advise Q-Mart about potential business implications (10 pts- 7 pts for hypothesis testing and 3 pts for business implications).

 

  • Suppose a Lightco produces light bulbs and wants to know whether it can claim that its light bulbs typically last more than 1500 hours. Hoping to find support for their claim, the firm collects a random sample of 25 lightbulbs and records the lifetime (in hours) of each bulb. The sample mean was 1509.5 hours with a sample standard deviation of 4.84. If you were to use 1 % significance level in this case, would you conclude that the mean life of the light bulbs is typically more than 1500 hours ? Please advise (10 pts- 7 pts for hypothesis testing and 3 pts for business implications).
  • Please open the Santa Fe Grill dataset on SPSS and answer the following questions.

 

6.a  The owners of the Santa Fe Grill want to find out whether their female customers have different opinions on several factors than their male customers: Fresh food (X_15), Food Taste (X_18), Friendly Employees (X_12). They are also curious whether it is the same for Jose’s customers. Set the hypothesis, report the SPSS analysis findings and advise Santa Fe Grill owners about potential implications (10 pts –  6 points setting the hypothesis and running the proper analysis, 4 points for the business advise).

 

  1. b The owners of the Santa-Fe Grill noticed that their customers may have a higher likelihood of returning to the restaurant (X_23) than recommending the restaurant to their family and friends (X_24). Since these two variables are likely to be related, they want to know if the ratings for likely to return are significantly higher (more favorable) than for recommending the restaurant. They also would like to know what Jose’s customers are inclined to do in the same case. Choose the appropriate statistical test that allows you to examine whether two means from these two different questions answered by the respondents are significantly different. Set the hypothesis, report the SPSS analysis findings and advise Santa Fe Grill owners about potential implications (15 pts – 10 points setting the hypothesis and running the proper analysis, 5 points for the business advise).

 

6.c Santa Fe Grill owners want to find out whether their advertisements make a difference in their customers’ satisfaction level (X22), likelihood to come back (X23), and likelihood to recommend (X24). They decided to ask their customers whether they remember the advertisements (X31_ad recall), they also ask them whether they are satisfied with the service (X22), likely to return (X23), and likely to recommend (X24). They want to see whether there are differences in the levels of satisfaction, likely to return, and likely to recommend between people who recall the ads and who do not recall the ads. Set the hypothesis, report the SPSS analysis findings and advise Santa Fe Grill owners about potential implications (15 pts – 10 points setting the hypothesis and running the proper analysis, 5  points for the business advise).

 

6.d. Santa Fe Grill owners want to find out whether their customers’ (a) likelihood to return (X23) and (b) likelihood to recommend (X24) the restaurant are different based on how far their customers travel to get to the restaurant. In other words, do statistically significant differences exist for X23 and X24 between all the distance driven customer groups, or only some? Set the hypothesis, report the SPSS analysis findings and advise Santa Fe Grill owners about potential implications (15 pts – 10 points setting the hypothesis and running the proper analysis,5  points for the business advise).