Exam 10: Confidence Intervals for Means

Compute the standard error of a sampling distribution. -Automobile mechanics conduct diagnostic tests on 150 new cars of particular make And model to determine the extent to which they are affected by a recent recall due to Faulty catalytic converters. They find 28% of the new cars tested do have faulty catalytic Converters. What is the standard error of the sampling distribution of the sample Proportion?

Use the Normal to model the distribution of sample proportions. -It is generally believed that electrical problems affect about 14% of new cars. An Automobile mechanic conducts diagnostic tests on 128 new cars on the lot. What is the Probability that in this group between 10% and 18% of the new cars will be found to have Electrical problems?

Compute the standard error of a sampling distribution. -Grandma Gertrude's Chocolates, a family owned business, has an opportunity to Supply its product for distribution through a large coffee house chain. However, the Coffee house chain has certain specifications regarding cacao content as it wishes to Advertise the health benefits (antioxidants) of the chocolate products it sells. Suppose Quality control inspectors at the coffee house chain take a sample of 100 pieces of this Chocolate product from an incoming shipment. They find a sample average of 60% cacao With a sample standard deviation of 8%. What is the standard error of the sampling Distribution of the sample mean?

Use the Normal to model the distribution of sample means. -A small business ships specialty homemade candies to anywhere in the world. Past Records indicate that orders weigh an average of 118 grams with a standard deviation of 14 grams. Suppose a random sample of 50 current orders is selected and each weighed And resulting sample mean is 110 grams. What is the probability of observing a sample Mean greater than 120 grams?

Use the Normal to model the distribution of sample proportions. -The owner of a pet store is trying to decide whether to discontinue selling specialty Clothes for pets. She suspects that only 4% of the customers buy specialty clothes for Their pets and thinks that she might be able to replace the clothes with more profitable Items. She decides to keep track of the customers who buy specialty clothes for their pets. If in a typical day there are 275 customers, would be it unusual for her to find that 21 Customers buy these specialty clothes?

Apply the Central Limit Theorem. -In a metal fabrication process, metal rods are produced that have an average length of 20.5 feet with a standard deviation of 2.3 feet. A quality control specialist collects a Random sample of 30 rods and measures their lengths. The sampling distribution of the Sample mean lengths is normally distributed with a mean of 20.5 feet and standard Deviation of 0.42. We can say this because

Use the Normal to model the distribution of sample proportions. -The owner of a small convenience store is trying to decide whether to discontinue Selling magazines. He suspects that only 5% of the customers buy magazines and thinks That he might be able to sell something more profitable. Before making a final decision, He keeps track of the number of customers who buy magazines on a given day. In a Typical day his store has 280 customers. Which of the following statements is (are) true About the sampling distribution of the sample proportion of customers who buy specialty Clothes for their pets at this store?

Compute the standard error of a sampling distribution. -A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. However the Pizza chain has certain specifications regarding the amount of cheese filling in its ravioli. Suppose quality control inspectors at this pizza restaurant chain sample 100 ravioli from An incoming shipment. They find a sample average of 16 grams with a standard Deviation of 1.8 grams. What is the standard error of the sampling distribution of the Sample mean?

Use the Normal to model the distribution of sample means. -A small business ships specialty homemade candies to anywhere in the world. Past Records indicate that orders weigh an average of 118 grams with a standard deviation of 14 grams. Suppose a random sample of 50 current orders is selected and each weighed And resulting sample mean is 110 grams. Which of the following statements is true?

Apply the Central Limit Theorem. -A small business ships specialty homemade candies to anywhere in the world. Past Records indicate that orders weigh an average of 118 grams with a standard deviation of 14 grams. Suppose a random sample of 50 current orders is selected and each weighed. The sampling distribution of the sample mean weights is normally distributed with a Mean of 118 grams and standard deviation of 1.98. We can say this because

Use the Normal to model the distribution of sample proportions. -The owner of a small convenience store is trying to decide whether to discontinue Selling magazines. He suspects that only 5% of the customers buy magazines and thinks That he might be able to sell something more profitable. Before making a final decision, He keeps track of the number of customers who buy magazines on a given day. In a Typical day his store has 280 customers. Would it be unusual for 28 customers to Purchase magazines?

Use the Normal to model the distribution of sample proportions. -According to a recent survey, about 33% of Americans polled said that they would Likely purchase reusable cloth bags for groceries in order to reduce plastic waste. Suppose 45 shoppers are interviewed a local supermarket. What is the probability that Between 28% and 38% of shoppers say that they are likely to purchase reusable cloth Bags for groceries?

Use the Normal to model the distribution of sample means. -In a metal fabrication process, metal rods are produced that have an average length of 20.5 feet with a standard deviation of 2.3 feet. A quality control specialist collects a Random sample of 30 rods and measures their lengths. What is the probability of Observing a sample mean greater than 21 feet?

Use the Normal to model the distribution of sample means. -In a metal fabrication process, metal rods are produced that have an average length of 20.5 feet with a standard deviation of 2.3 feet. A quality control specialist collects a Random sample of 30 rods and measures their lengths. Suppose the resulting sample mean Is 19.5 feet. Which of the following statements is true?

Use the Normal to model the distribution of sample proportions. -The owner of a pet store is trying to decide whether to discontinue selling specialty Clothes for pets. She suspects that only 4% of the customers buy specialty clothes for Their pets and thinks that she might be able to replace the clothes with more profitable Items. In a typical day there are 275 customers. Which of the following statements is (are) true about the sampling distribution of the sample proportion of customers who buy Specialty clothes for their pets at this store?

Compute the standard error of a sampling distribution. -A recent survey of 120 senior citizens at a local supermarket found that 44% have Purchased reusable cloth bags for groceries. What is the standard error of the sampling Distribution of the sample proportion?

Use the Normal to model the distribution of sample proportions. -It is generally believed that electrical problems affect about 14% of new cars. An Automobile mechanic conducts diagnostic tests on 128 new cars on the lot. What is the Probability that in this group over 18% of the new cars will be found to have electrical Problems?

Use the Normal to model the distribution of sample means. -A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on Data collected from its automatic filling process, the amount of cheese inserted into the Ravioli is normally distributed with a mean of 15 grams and standard deviation of 0.15 Grams. To make sure that the automatic filling process is on target, quality control Inspectors take a sample of 25 ravioli and measure the weight of cheese filling. What is The standard deviation of the sampling distribution of the sample mean weight?

Use the Normal to model the distribution of sample means. -Grandma Gertrude's Chocolates, a family owned business, has begun making a new Line of chocolates with high levels of cacao so it can advertise its health benefits of Antioxidants. The product with the highest % cacao at Grandma Gertrude's Chocolates Averages 45% cacao with a standard deviation of 6 %. Suppose a sample of 36 pieces of This chocolate is taken from the production line. What is the standard deviation of the Sampling distribution of the sample mean?

Use the Normal to model the distribution of sample proportions. -According to a recent survey, about 33% of Americans polled said that they would Likely purchase reusable cloth bags for groceries in order to reduce plastic waste. Suppose 45 shoppers are interviewed a local supermarket. What is the probability that no More than 28% of shoppers say that they are likely to purchase reusable cloth bags for Groceries?