A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but now are beginning to increase in price because of added features. According to the story, the average price of all digital cameras a couple of years ago was $215.00. A random sample of n = 200 cameras was recently taken and entered into a spreadsheet. It was desired to test to determine if that average price of all digital cameras is now more than $215.00. α = 0.1
525 is the right answer
First, what is the sample mean and standard deviation? No spreadsheet given. Cannot copy and paste here.
To test the hypothesis that the average price of all digital cameras is now more than $215.00, you can follow these steps:
Step 1: State the null hypothesis (H0) and the alternative hypothesis (Ha):
H0: The average price of all digital cameras is less than or equal to $215.00.
Ha: The average price of all digital cameras is greater than $215.00.
Step 2: Determine the significance level (α):
The given significance level is α = 0.1.
Step 3: Calculate the sample mean and sample standard deviation:
From the sample of n = 200 digital cameras, calculate the sample mean (x̄) and sample standard deviation (s).
Step 4: Perform a one-sample t-test:
Calculate the test statistic t using the formula:
t = (x̄ - μ) / (s / √n)
where x̄ is the sample mean, μ is the hypothesized population mean (μ = $215.00), s is the sample standard deviation, and n is the sample size.
Step 5: Determine the critical value:
Find the critical value (tcrit) from the t-distribution table corresponding to a one-tailed test with α = 0.1 and (n - 1) degrees of freedom.
Step 6: Compare the test statistic with the critical value:
If t > tcrit, reject the null hypothesis and conclude that the average price of all digital cameras is now more than $215.00. Otherwise, fail to reject the null hypothesis.
Step 7: Calculate the p-value (optional):
If the software or calculator used provides the p-value, calculate it using the t-distribution and compare it with α. If the p-value is less than α, reject the null hypothesis.
Remember to refer to the specific t-distribution table and its degrees of freedom values to obtain the exact critical value in Step 5.
To test whether the average price of all digital cameras is now more than $215, we can perform a hypothesis test.
Step 1: Formulate the Null and Alternative Hypotheses
The null hypothesis (H0) is that the average price of all digital cameras is still $215 or less. The alternative hypothesis (Ha) is that the average price is now more than $215.
H0: μ ≤ $215
Ha: μ > $215
Step 2: Determine the Significance Level (α)
The significance level (α) is given as 0.1. This represents the maximum risk of rejecting the null hypothesis when it is true.
Step 3: Collect and Analyze the Data
A random sample of n = 200 digital cameras has been taken and recorded. We can calculate the sample mean (x̄) and the sample standard deviation (s) from this data.
Step 4: Calculate the Test Statistic
We will use the t-test since the population standard deviation is unknown. The test statistic (t) can be calculated using the formula:
t = (x̄ - μ) / (s / √n)
where x̄ is the sample mean, μ is the assumed population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size.
Step 5: Determine the Critical Value
To determine the critical value for a one-tailed test at α = 0.1, we need to find the t-value corresponding to the upper 90th percentile with (n - 1) degrees of freedom.
Step 6: Make a Decision
If the calculated test statistic (t) is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject it.
Step 7: Interpret the Results
If we reject the null hypothesis, we can conclude that there is evidence to suggest that the average price of all digital cameras is now more than $215. If we fail to reject the null hypothesis, we do not have enough evidence to conclude that the average price has increased.
Please provide the sample mean (x̄), sample standard deviation (s), and the critical t-value to continue with the calculation and the decision-making process.