The manufacturer of a new compact car claims that the car will average at least
ID: 3312638 • Letter: T
Question
The manufacturer of a new compact car claims that the car will average at least 35 miles per gallon in general highway driving.
For 100 test runs, the car averaged 35.5 miles per gallon with a standard deviation of 4 miles per gallon.
Suppose that the manufacturer tests the following hypotheses:
Consider the 10% significance level. What is the power of the test if the actual average fuel efficiency is 36 miles per gallon?
The sales manager of a food company wants to determine if the weekly sales of 16 ounce packages of frozen broccoli has increased since last year. The mean weekly number of sales per store was 2,400 packages last year. The sales manager set the following hypotheses to test
Available sales data are from 400 stores. Assume that this data set is a random sample. The sample mean is 2,440 and the sample standard deviation is 800. For the significance level of 1%, find the critical value.
The manager of a firm wants to determine if the average hourly wage for semi-skilled workers is $9 in the Capital District.
In order to do so, she takes a random sample of 100 hourly wages and finds that the sample mean is $8 and the sample standard deviation is $2.
The hypotheses to be tested are:
Assume that the actual average is $8.8. What is the probability of type II error at the 5% significance level?
A government agency receives many consumer complaints that the boxes of detergent sold by a company contain less than the 20 oz of detergent advertised.
To check the consumers' complaints, the agency purchases 100 boxes of the detergent and finds that the sample mean is 19.4 oz and the sample standard deviation is 4 oz.
The agency conducts a testing of the following hypotheses at the 10% level of significance:
What is the p-value and the result of the hypothesis testing?
Explanation / Answer
As per the chegg policy we are advised to do only one question at a time so I am attempting the second one.
In this, we don't know the population standard deviation so we will use the t-distribution here.
Degrees of freedom = n - 1 = 400 - 1 = 399
Also the alternative hypothesis contains greater than sign so this would be a right tailed test.
Hence,
Critical value at 1% significance level = 2.3357
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