Evaluating Claims Sampling Distributions HW

Identify the population

• 20 game pieces

• p = 25%

• p-hat = 15%

• All game pieces

Identify the sample

• 20 game pieces

• 25%

• 3 instant winners

• All game pieces

Identify the parameter

• 20 game pieces

• p = 25%

• 3 instant winners

• p-hat = 3/20 = 15%

Identify the statistic

• 20 game pieces

• p = 25%

• 3 instant winners

• p-hat = 3/20 = 15%

What does the dot above .05 represent?

• 5% of the sample proportions had 1 instant winner out of 20.

• In a single sample of 20 game pieces, 1/20 (5%) were instant winners.

• There is a .05 chance of getting 1 instant winner in a sample of 20 pieces.

Would it be unusual to get a sample proportion of .35 or higher? Explain

• Yes because only 10 of the sample proportions 0.35.

• No because 23/100 of the sample proportions were 35% or higher. 23% is not unusual

• Yes because we should get 25% every time.

Would it be unusual to get a sample proportion of .60 or higher? Explain

• Yes because only 1 out the 100 sample proportions was 60%. 0.01 is unusual.

• Yes because if it is possible, it can't be unusual.

The actual sample proportion was 3/20 = 0.15. Is this convincing evidence that fewer than 25% of the game pieces are instant winners?

• Yes because only 5 of the sample proportions were less than 15%. 5/100 = 5% which is low.

• No because 19/100 sample proportions gave a proportion of 15% or lower. 19% is not considered unusual.

• Yes because we should have gotten a sample proportion of 25% if that is actually the proportion of instant winners.

A large pet store claims that the lengths of its guppies are normally distributed with a mean of 5 cm and a standard deviation of 0.5 cm. You come to the store and buy 10 guppies. The mean length of your sample is only 4.8 cm. The dotplot shows a simulated distribution of sample means from 200 random samples. Is there evidence that the true mean length is actually less than 5 cm?

• Yes. In 4 samples, the mean was 4.8 or less. 4/200 = 2% which is unusually low.

• Yes. In 21 samples, the mean was 4.8 or less. 11.5% is not unusually low.

• Yes. In 21/ 200 samples, the mean was 4.8 or less. 11.5% is usually low.

• No. In 21/ 200 samples, the mean was 4.8 or less. 11.5% is not unusually low.

A distribution showing the sample means of all sample of size n of a population is called

• Normal Distribution
• Binomial Distribution
• Sampling Distribution
• Uniform Distribution