Essay What is the Point Estimate of the Population Mean – Statistics Assignment Help

Assignment Task:

Task:

1. The Simcoe County Food Emporium claims that “the typical customer spends $60 per visit.” A sample of 12 customers revealed the following purchases, in dollars, spent last visit: $64 66 64 66 59 62 67 61 64 58 54 66

a. What is the point estimate of the population mean?

b. Develop a 90% confidence interval for the population mean. c. Is the restaurant’s claim that the “typical customer” spends $60 per visit reasonable? Justify your answer.

2. Marty Rowatti recently assumed the position of director of the YMCA. He would like some current data on how long current members of the YMCA have been members. To investigate, suppose he selects a random sample of 40 current members. The mean length of membership of those included in the sample is 8.32 years and the standard deviation is 3.07 years. a. What is the mean of the population? b. Develop a 90% confidence interval for the population mean.

c. The previous director, in the summary report she prepared as she retired, indicated the mean length of membership was now “almost 10 years.” Does the sample information substantiate this claim? Explain your reasoning.

3. The proportion of public accountants who have changed companies within the last three years is to be estimated within 3%. The 95% level of confidence is to be used. A study conducted several years ago revealed that the percentage of public accountants changing companies within three years was 21.

a. To update this study, the files of how many public accountants should be studied?

b. How many public accountants should be contacted if no previous estimates of the population proportion are available? Chapter 9:

4. For each of the following, state the null hypothesis and the alternative hypothesis:

a. The publisher of Celebrity Living claims that the mean sales of personality magazines featuring such celebrities as Angelina Jolie or Kim Kardashian is at least 1.5 million per week. A sample of 10 comparable titles shows that the mean weekly sales last week was 1.3 million. The publisher’s claim is to be verified.

b. The manager of Little Cakes Inc. states that an average of 1500 muffins is sold each week in the retail store. One of the bakers feels that the average is less than 1500 and decides to test this claim.

c. For the past three years, an insurance company has stated that its average claim amount is $2000. The manager feels that this amount should be updated and takes a sample of 55 claims to see if there is a difference in the average claim amount.

d. A machine on a production line is set to automatically fill each bottle with 500 mL of water. The quality control manager regularly takes random samples of the bottles from the production line to ensure that the machine is filling the bottles correctly. If not, the machine will need adjusting. Statistics Assignment #2 Due: June 22, 2021 5. At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average more than $80 a day in tips.” Assume that the population of daily tips is normally distributed, with a standard deviation of $3.24. Over the first 35 days she was employed at the restaurant, the mean daily amount of her tips was $84.65. At the 0.01 significance level, can Ms. Brigden conclude that her daily tips average more than $80?

6. A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the 0.03 significance level: H0: µ ≥ 220 H1: µ < 220 Chapter 14:

7. Classic Gold Inc. manages five golf courses. The director of golf for Classic Golf Inc. wishes to study the number of rounds of golf played per weekday at the five courses. He gathered the following sample information for 520 rounds: Day Rounds Monday 124 Tuesday 74 Wednesday 104 Thursday 98 Friday 120 At the 0.05 significance level, is there a difference in the number of rounds played by day of the week?

8. Professor Brown has been teaching Statistics 201 for 20 years. In the past, student grades for the 40 students in his classes have been distributed with the breakdown shown in the following table in the column labelled “Statistics 201.” His fall class last semester achieved the grades as shown in the column labelled “Fall Class.” At the 0.05 level of significance, is there is difference in the distribution of grades for his fall class?