T-TEST

Problem 1:

A nutritionist claims that a serving of their new "Healthy Potato Snack" contains an average of 150 calories. A random sample of 25 servings was analyzed, and the results showed an average of 155 calories with a standard deviation of 12 calories. Test whether there is significant evidence to suggest the average calorie content is different from the nutritionist's claim.

Step 1: Define null (Ho) and alternative (Ha)

Ηο: μ = 150 (The average calorie content is 150 calories)

Ηa: μ ≠ 150 (The average calorie content is different from 150 calories) 

Step 2: Determine sample size (n), sample mean (x̄), population mean (μ), standard deviation (s), and a= 0.05 (95% confidence level) 

Given:

significance level a = 0.05 (95% confidence level) 

sample size (n) = 25

sample mean (x̄) = 155 

population mean (μ) = 150 

standard deviation (s) = 12 

Step 3: Calculate the t-value using the formula. (You can use the t-test calculator provided to verify your answer.) 

The t-value is 2.08333333.

Step 4: Determine degrees of freedom (df). (You can use the t-test calculator provided to verify your answer.) 

Formula of df: df=n-1 

df= 25-1 

df= 24 

Step 5: Find the critical t-value. (You can use the t-test calculator provided to verify your answer.) 

Using a t-table for df = 24 and α = 0.05 (two-tailed test), the critical t-value is approximately ±2.064. 

Step 6: Make a decision, reject or fail to reject the null hypothesis.

Decision: Since the calculated t-value (2.08333333) is greater than the critical value (2.064), we reject the null hypothesis. 

Conclusion: There is significant evidence to suggest that the average calorie content of the "Healthy Potato Snack" is different from 150 calories.

TRY THIS!

Instruction: Solve the following problems, then verify your answers using the t-test calculator provided.

Problem 1:

A manufacturer of "Honey-Infused Cucumber Bites" states that the average weight of each bite is 20 grams. A quality control team randomly selects 30 bites and finds an average weight of 19.5 grams with a standard deviation of 1.8 grams. Determine if there is sufficient evidence to conclude that the average weight of the bites is significantly less than the manufacturer's claim.

Problem 2:

A company producing "Organic Honey-Glazed Carrots" claims that each package contains an average of 80 grams of carbohydrates. A consumer advocacy group suspects the actual carbohydrate content is different. They randomly select 18 packages and find the average carbohydrate content to be 83 grams, with a standard deviation of 9 grams. Test if there is sufficient evidence to support the consumer group's suspicion.

Problem 3:

A sports brand claims that their latest running shoes last an average of 600 kilometers before wearing out. A random sample of 28 pairs was tested, revealing an average durability of 590 kilometers with a standard deviation of 25 kilometers. Test at α = 0.05 if the actual durability differs from the claim.

Problem 4:

A well-known sportswear company advertises that their newest model of running shoes can withstand an average of 600 kilometers before showing significant signs of wear and tear. To test this claim, a group of researchers randomly selected 28 pairs of these shoes and subjected them to real-world running conditions. After the experiment, the results showed that the shoes lasted an average of 590 kilometers, with a standard deviation of 25 kilometers.

Problem 5:

A farmer claims that the average weight of their "Jumbo Baked Potatoes" is 300 grams. A grocery store chain, looking to purchase these potatoes, takes a random sample of 20 potatoes and finds the average weight to be 285 grams, with a standard deviation of 25 grams. Does the grocery store's sample provide enough evidence to suggest that the average weight of the potatoes is significantly different from the farmer's claim?