statistics
posted by mariha .
One important task in experiment design is to determine the sample size needed to support the conclusion. A manufacturer for a specific assistive device claims that its battery can last longer than 15 days without recharging. To check if this claim is valid, a hypothesis test is conducted: H0: u≤15, Ha: u>15, and the significance level for the test is set to be 0.05. Let assume that the standard deviation sigma=1.6.
(a) Explain what Type I error and Type II error that may occur in this study.
(b) What is the probability of committing a type II error if its battery actual last for 14 days.
(c) What sample size you will need if it is intended for a 90% probability of detecting that ‘the u is less than 15’ when it was actually u=14.

Here are a few suggestions:
Type I errors result when you reject the null and it's true. Type II errors result when you accept the null and it's false. The probability of a Type II error is beta.
You may be able to find sample size using margin of error.
Formula is this:
Margin of error = (zvalue)(sd/√n)
Respond to this Question
Similar Questions

statistics
Determine the sample size required to estimate a population proportion to within 0.032 with 95.7% confidence, assuming that you have no knowledge of the approximate value of the sample proportion. Sample Size = B. Repeat part the previous … 
statistics
A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 4% margin of error at a 99% confidence level, what size of sample is needed? 
STATISTICS
Length of Hospital Stays: The average length of “short” hospital stays for men is slightly longer thatn that for women: 5.2 days vs. 4.5 days. A random sample of recent hospital stays for both men and women revealed the following. … 
statistics
Suppose a manufacturer claims that each familysize bag of pretzels sold weighs 12 ounces on average with a standard deviation of 0.8 ounces. A consumer's group decides to test this claim. If a simple random sample of 49 bags of pretzels … 
statistics
An IQ is designed so that the mean is 100 and the standard deviation is 23 for the population of Normal adults, find the sample size necessary to estimate the mean IQ score of statistics students Such that it can be said with 90% confidence … 
economics 7
An electronics company advertises that the battery life of its new smart phone with normal usage averages 72 hours. The company says this is one of the desirable characteristics of the phone which makes the phone a better choice compared … 
economics
An electronics company advertises that the battery life of its new smart phone with normal usage averages 72 hours. The company says this is one of the desirable characteristics of the phone which makes the phone a better choice compared … 
economics (7)
An electronics company advertises that the battery life of its new smart phone with normal usage averages 72 hours. The company says this is one of the desirable characteristics of the phone which makes the phone a better choice compared … 
Sciene
Portfolio: you will design an experiment to investigate the relationship between the number of coil loops and the strength of a solenoid. One you have an experiment plan, carry out your experiment and record data. After finishing conducting … 
statistics
A consumer advocacy group claims that the mean amount of juice in a 16 ounce bottled drink is not 16 ounces, as stated by the bottler. Determine the conclusion of the hypothesis test assuming that the results of the sampling lead to …