2) SLT Mobitel would like to test the hypothesis that the average revenue per retail user for Etisalat's customers equals $50. A random sample of thirty two Etisalat's customers provided an average revenue of $54.70. The population standard deviation for the revenue per retail user is believed to be $11.00. SLT Mobitel would like to set an alpha level of 0.05. Test this hypothesis using the critical value approach.
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- A manufacturer of kitchen water filters claims that their new model of water filter will, on average, treat more than 500 gallons of water before the water quality falls below acceptable levels. Consumer Reports wants to confirm this claim and selects a simple random sample of 60 filters for testing. Water was passed through each filter until the water quality dropped below acceptable levels and the volume of water measured. This produced a sample average of 575 gallons, and a sample standard deviation of 60 gallons. Construct a null and alternate hypothesis that Consumer Reports should use to confirm the manufacturer’s claim. Based on the sample data, what can they conclude? Use a 0.05 level of significance. Would your answer change if you used a 1% level of significance?A fish hatchery manager estimates that on average fisherpersons catch 3.5 fisheach fishing trip. A random sample of 10 fisherpersons showed they caught 3.9 fishper trip, with a standard deviation of 1.7 fish per trip. Perform a test of hypothesisat a 0 .10 alpha level to determine whether or not her claim is true. Use a two tailedtest of hypothesis and the critical value method.The Transportation Security Administration would like to compare the average amount of time it takes passengers to pass through airport security at Philadelphia versus Orlando during peak times. A random sample of 25 travelers in Philadelphia spent an average of 14.6 minutes to pass through airport security with a sample standard deviation of 5.8 minutes. A random sample of 27 travelers in Orlando spent an average of 11.5 minutes to pass through airport security with a sample standard deviation of 4.9 minutes. Perform a hypothesis test using α = 0.05 to determine if the average time to pass through security in Philadelphia is more than the average time to pass through security in Orlando. Assume the population variances for time through security at these two locations are equal. Hint: the alternative hypothesis should be μ1 - μ2 > 0.
- A journal reported that the average screen time of teenagers is 6.77 hours per week. You gathered 30 independent samples from your class and obtained an average screen time of 7.8 hours per week, with a sample standard deviation of 2.9 hours. At alpha = 0.10, is this enough evidence to say that the average screen time of your class is higher than the reported screen time? What is the mean value for the null hypothesis?In a certain year, the average annual family income in the National Capital Region was P310,860 with a standard deviation of P176,870. With the increased prices of commodities, it is hoped that the mean annual family income has also increased. A survey is conducted to verify this claim. A random sample of 320 families has a mean annual income of P325,255. Which is the most appropriate null hypothesis to choose?A manufacturer of air conditioners seeks to ensure that their air conditioners are efficient enough that they will use no more than 2800 watt/hr under typical usage.The quality control department has tested a sample of 63 air conditioner units and found an average energy use of 7000 watts/hr. From previous tests, it can safely be assumed that the population standard deviation is 10000 watts/hr. Use the p-value approach and a 0.01 level of significance to test to see if the air conditioners are using too much energy. What is the P value?
- In attempting to improve student services, a college investigates its registration process and finds that for 12 randomly selected students, the mean registration time was 73.2 minutes with a standard deviation of 14.2 minutes. Another college finds that for 15 randomly selected students, the mean registration time was 42.3 minutes with a standard deviation of 9.8 minutes. At the 0.01 significance level, test the claim that the two samples came from populations with the same means. Assume equal population variances.The average expenditure per student (based on average daily attendance) for a certain school year was $10,337 with a population standard deviation of $1560. A survey for the next school year of 150 randomly selected students resulted in a sample mean of $10, 798. Find the P-value? Should the null hypothesis be rejected at alpha = .05 level of significance?For each shipment of parts, a manufacturer wants to accept only those shipments with at most 10% defective parts. A large shipment has just arrived. A quality control manager randomly selects 55 of the parts from the shipment and finds that 6 parts are defective. Use a .05 level of significance to conduct the appropriate hypothesis test. Which of the following conclusions is true? there is insufficient evidence at alpha = 0.05 to reject the entire shipment there is sufficient evidence at alpha = 0.05 to reject the entire shipment the population proportion standard deviation is needed to do the test because of the large sample size the test cannot be done since the population proportion distribution is not normal
- 2. The Acme Company manufactures large capacity Flash drives using two different manufacturing processes. The company is interested in determining if there is a significant difference in the average manufacturing time of the two processes. For Process #1, a sample of 28 items shows a sample mean of 9 minutes and a sample standard deviation of 3.5 minutes. For Process #2, a sample of 23 items shows a sample mean of 13 minutes and a sample standard deviation of 4.5 minutes. At a 5% level of significance, Test the claim of no difference in the average time for the two processes. What is your conclusion?A company makes a device that can be fitted to car engines to improve their fuel efficiency. The company asserts that when the device is installed drivers should experience a mean increase of more than 3kilometres per litre. Assuming that the population standard deviation of increase is known to be 0.75kilomtres per litre and a sample size of 64 cars is selected with a mean of 3.25kilometres per litre, use the p-value approach to test the null hypothesis using a significance level of 0.05.An economist collects a simple random sample of 32 teachers salaries in Cititon, and finds a mean of $67,000 and a standard deviation of $8,000. Is there enough evidence to conclude, at a significance of alpha = 0.05, that the mean salary of teachers in Cititon is different than $70,000? What is the claim? What is the null hypothesis? What is the alternative hypothesis? What is the test statistic? What is/are the critical value(s)? Do we reject the null hypothesis? What conclusion do we draw? What is the P-value for the problem above?