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[answered] 1.One year consumers spent an average of $22 on a meal at a


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1.One year consumers spent an average of $22 on a meal at a resturant. Assume that the amount spent on a resturant meal is normally distributed and that the standard deviation is $6. Complete parts (a) through (c) below. a. What is the probability that a randomly selected person spent more than $23?

 

P(X>$23)= (Round to four decimal places as needed.) b. What is the probability that a randomly selected person spent between $9 and $18?

 

P($9<Xl<$18)= (Round to four decimal places as needed.) c. Between what two values will the middle 95% of the amounts of cash spent fall? The middle 95% of the amounts of cash spent will fall between X=$ and X=$ .(Round to the nearest cent as needed.) 2.A market researcher selects a simple random sample of n=100 users of a social media website from a population of over 100 million registered users. After analyzing the sample, she states that she has 95% confidence that the mean time spent on the site per day is between 15 and 57 minutes. Explain the meaning of this statement.

 

Choose the correct answer below. A.During any given day there is a 95% chance that the mean time all registered users spent on the site was between 15 and 57 minutes. B.There is a 95% chance that a randomly selected registered user spends between 15 and 57 minutes on the site per day. C.Of the over 100 million registered users, 95% of them spend between 15 and 57 minutes on the site per day. D.One is 95% confident that the true mean time all registered users spend on the site per day is between 15 and 57 minutes. 3.In a study of 425 nonprofits nationwide, 80 indicated that turnover has been the biggest employment challenge at their organization. Complete parts (a) through (c). a. Construct a 95% confidence interval for the population proportion of nonprofits that indicate turnover as

 

. the biggest employment challenge at their organization. l? ? ? (Type integers or decimals. Round to three decimal places as

 

needed.) b. Interpret the interval constructed in part (a) . .

 

Choose the correct answer below. A.With 95% confidence, the proportion of nonprofits that indicate turnover as the biggest employment challenge at their organization in the sample is in this interval. B.With 5% confidence, the proportion of nonprofits that indicate turnover as the biggest employment challenge at their organization in the population is in this interval. C.With 95% confidence, the proportion of nonprofits that indicate turnover as the biggest employment challenge at their organization in the population is in this interval. D.With 5% confidence, the proportion of nonprofits that indicate turnover as the biggest employment challenge at their organization in the sample is in this interval. c.. If you wanted to conduct a follow?up study to estimate the population proportion of nonprofits that indicate turnover as the biggest employment challenge at their organization to within plus or minus ?0.04 with 95 % confidence, how many nonprofits would you survey? A sample of nonprofits should be surveyed. (Round up to the nearest integer.)?? 4.According to a social media blog, time spent on a certain social networking website has a mean of 17 minutes per visit. Assume that time spent on the social networking site per visit is normally distributed and

 

that the standard deviation is 6 minutes. Complete parts (a) through (d) below. a. If you select a random sample of 25 sessions, what is the probability that the sample mean is between

 

16.5 and 17.5 minutes? (Round to three decimal places as needed.) b. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 16 and 17 minutes? (Round to three decimal places as needed.) c. If you select a random sample of 100 sessions, what is the probability that the sample mean is between 16.5 and 17.5 minutes? (Round to three decimal places as needed.) d. Explain the difference in the results of (a) and (c). The sample size in (c) is greater than the sample size in (a), so the standard error of the mean (or the standard deviation of the sampling distribution) in (c) is than in (a). As the standard error greater or less values become more concentrated around the mean. Therefore, the probability that the

 

decrease or increase sample mean will fall in a region that includes the population mean will always when the decrease or increase sample size increases. 5.The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 84 hours. A random sample of 49 light bulbs indicated a sample mean life of 320 hours. Complete parts (a) through (d) below. a. Construct a 95% confidence interval estimate for the population mean life of light bulbs in this shipment.

 

The 95% confidence interval estimate is from a lower limit of hours to an upper limit of hours.(Round to one decimal place as needed.) b. Do you think that the manufacturer has the right to state that the lightbulbs have a mean life of 370 hours? Explain.

 

Based on the sample data, the manufacturer or has the right to state that the lightbulbs does not have have a mean life of 370 hours. A mean of 370hours is or more than 4 standard errors less than 2 the sample mean, so it is below or above or highly unlikely that the lightbulbs have a mean likely life of 370 hours. c. Must you assume that the population light bulb life is normally distributed? Explain.

 

A.Yes, the sample size is too large for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem.

 

B.No, since ? is known and the sample size is large enough, the sampling distribution of the mean is approximately normal by the Central Limit Theorem.

 

C.No, since ? is known, the sampling distribution of the mean does not need to be approximately normally

 

distributed.

 

D.Yes, the sample size is not large enough for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem. d. Suppose the standard deviation changes to 63 hours. What are your answers in (a) and (b)?

 

The 95% confidence interval estimate would be from a lower limit of limit of hours to an upper hours.(Round to one decimal place as needed.) Based on the sample data and a standard deviation of 63 hours, the manufacturer or has

 

does not the right to state that the lightbulbs have a mean life of 370 hours. A mean of 370 hours is more than 5 or less than 2 standard errors above or belowthe sample mean, so it is likely or highly unlikely that the lightbulbs have a mean life of 370 hours. 6.If n=400 and X=80, construct a 99% confidence interval estimate of the population proportion. ? ? ? (Round to four decimal places as needed.) 7.If the manager of a bottled water distributor wants to estimate, with 95% confidence, the mean amount of water in a 1?gallon bottle to within plus or minus ? 0.003 gallons and also assumes that the standard deviation is 0.02 gallons, what sample size is needed?n= (Round up to the nearest integer.) 8.Assuming that the population is normally distributed, construct a 99% confidence interval for the population mean for each of the samples below. Explain why these two samples produce different confidence intervals even though they have the same mean and range.

 

Sample A:

 

1

 

1???

 

1???

 

3

 

6???

 

8

 

8???

 

8 Sample B:

 

1

 

2???

 

3

 

4???

 

5

 

6???

 

7 8

 

Construct a 99% confidence interval for the population mean for sample A. less than or ? ? ? (Type integers or decimals rounded to two decimal places as needed.)

 

Construct a 99% confidence interval for the population mean for sample B.

 

nothing less than or ? ? ?

 

nothing (Type integers or decimals rounded to two decimal places as needed.)

 

Explain why these two samples produce different confidence intervals even though they have the same mean and range.

 

A.The samples produce different confidence intervals because their standard deviations are different.

 

B.The samples produce different confidence intervals because their critical values are different.

 

C.The samples produce different confidence intervals because their sample sizes are different.

 

D.The samples produce different confidence intervals because their medians are different.

 


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