Question

In: Statistics and Probability

300 air conditioners were tested and it was found that the average power usage per hour...

300 air conditioners were tested and it was found that the average power usage per hour during the summer months (for around 9 hours per day) is 4200 W. Find the 95% confidence interval if sigma = 100 W.

Expert Solution

Solution :

Given,

= 4200

= 100

n = 300

Note that, Population standard deviation() is known..So we use z distribution.

Our aim is to construct 95% confidence interval.

c = 0.95

= 1- c = 1- 0.95 = 0.05

/2 = 0.05 2 = 0.025 and 1- /2 = 0.975

Search the probability 0.975 in the Z table and see corresponding z value

= 1.96

The margin of error is given by

E = /2 * ( / n )

= 1.96 * ( 100/ 300 )

= 11.316

Now , confidence interval for mean() is given by:

( - E ) < < ( + E)

( 4200 - 11.316 ) < < ( 4200 + 11.316 )

4188.684 < < 4211.316

Required 95% confidence interval is ( 4188.684 , 4211.316 )

orchestra answered 1 year ago

150 air conditioners were tested and it was found that the average power usage per hour...

150 air conditioners were tested and it was found that the average power usage per hour during the summer months (for around 9 hours per day) is 3800 W. Find the 90% confidence interval if sigma = 80 W.

Average power usage (in dB per hour) for a particular company is studied and it is...

Average power usage (in dB per hour) for a particular company is studied and it is found to have a lognormal distribution with parameters μ = 4 and σ = 2. (a) What is the probability that the company uses more than 235.1 dB during any particular hour? (b) Find the 15.39-th percentile of the power usage for this company during any partic- ular hour. (c) How much power is this company expected to use during any particular hour?

Cloud air conditioners cost $300 to purchase, result in electricity bills of $150 per year, and...

Cloud air conditioners cost $300 to purchase, result in electricity bills of $150 per year, and last for 5 years. Luxury Air models cost $500, result in electricity bills of $100 per year, and last for 8 years. The discount rate is 21 percent. a. What are the equivalent annual costs of the Cloud and Luxury Air models? Which model is more cost effective? b. Now you remember that the inflation rate is expected to be 10 percent per year...

Econo-cool air conditioners cost $300 to purchase, result in electricity bills of $150 per year, and...

Econo-cool air conditioners cost $300 to purchase, result in electricity bills of $150 per year, and last for 5 years. Luxury Air models cost $500, result in electricity bills of $100 per year, and last for 8 years. The discount rate is 21 percent. a. What are the equivalent annual costs of the Econo-cool and Luxury Air models? Which model is more cost effective? b. Now you remember that the inflation rate is expected to be 10 percent per year...

In order to estimate the average electric usage per month, a sample of 47 houses were...

In order to estimate the average electric usage per month, a sample of 47 houses were selected and the electric usage determined. The sample mean is 2,000 KWH. Assume a population standard deviation of 142 kilowatt hours. At 90% confidence, compute the margin of error? In order to estimate the average electric usage per month, a sample of 46 houses were selected and the electric usage determined. The sample mean is 2,000 KWH. Assume a population standard deviation of 127...

Tracy Company, a manufacturer of air conditioners, sold 300 units to Thomas Company on November 17,...

Tracy Company, a manufacturer of air conditioners, sold 300 units to Thomas Company on November 17, 2021. The units have a list price of $275 each, but Thomas was given a 20% trade discount. The terms of the sale were 2/10, n/30. Thomas uses a perpetual inventory system. Required: 1. Prepare the journal entries to record the (a) purchase by Thomas on November 17 and (b) payment on November 26, 2021. Thomas uses the gross method of accounting for purchase...

A retail outlet for air conditioners believes that its weekly sales are dependent upon the average...

A retail outlet for air conditioners believes that its weekly sales are dependent upon the average temperature during the week. The outlet picks, at random, 12 weeks during the year and records the number of air conditioners that are sold and the average temperature that week. The data is below. Temp (in deg.) Sales (# of conditioners) 72 3 77 4 82 7 43 1 31 0 28 0 81 8 83 ...

In a recent study, 5 Japanese and 6 U.S. plants that manufacture air conditioners were sampled...

In a recent study, 5 Japanese and 6 U.S. plants that manufacture air conditioners were sampled and their turnover rates determined. The Japanese plants had a mean turnover of 3.12 percent with a standard deviation of 1.23 percent. The U.S. plants had a mean turnover of 6.30 percent with a standard deviation of 1.26 percent. Use this data and test whether there is a population difference in percent turnover between Japanese and U.S. air conditioning manufacturers 1. Find the Critical...

It is assumed that there is an average of 12 customers per hour at a service...

It is assumed that there is an average of 12 customers per hour at a service counter according to a Poisson process. a) How likely is it that 4 customers show up at this counter in the next 15 minutes? b) Given that 4 customers showed up at this counter in a given 15-minute period, what is the probability that there were at least 2 customers that showed up in the last 5 minutes of this period?

A house has an air infiltration rate of 0.300 air exchanges per hour. During an episode...

A house has an air infiltration rate of 0.300 air exchanges per hour. During an episode of photochemical smog, the outdoor concentration of peroxyacetyl nitrate (PAN) is 79.6 ppb. If the family remains indoors, and the initial concentration of PAN inside is 12.1 ppb, how long (in hours) will it be before the PAN concentration inside rises to 39.0 ppb?