A manufacturer of toasters claims that the toasters have a mean life of 9 years and a standard deviation of 2.1 years. A random sample of 60 such toasters is selected for testing.
Assume all samples are simple random samples and α (alpha) is taken to be 0.05.
To test the manufacturer's claim, we need to set up the null hypothesis and the alternative hypothesis.
Null hypothesis (H0): The mean life of the toasters is 9 years.
Alternative hypothesis (H1): The mean life of the toasters is different from 9 years.
Based on the given information, the population mean (μ) is 9 years and the population standard deviation (σ) is 2.1 years.
Since we do not know the population standard deviation, we will conduct a t-test using the sample mean and the sample standard deviation.
The sample size is 60 (n = 60), which is greater than 30, allowing us to use the t-distribution.
With a significance level of α = 0.05, we will reject the null hypothesis if the p-value is less than 0.05.
To proceed with the t-test, we need to calculate the test statistic (t-score) and the corresponding p-value.
The test statistic (t-score) can be calculated using the formula:
t = (x̄ - μ) / (σ / √n)
Where:
x̄ is the sample mean
μ is the population mean
σ is the population standard deviation
n is the sample size
Given that x̄ (sample mean) is not provided, we cannot calculate the test statistic.
Please provide the sample mean (x̄) in order to proceed with the t-test.