Sampling Distribution Counts

In the game of Scrabble, each player begins by drawing 7 tiles from a bag containing 100 tiles. There are 42 vowel, 56 consonants, and 2 blank tiles in the bag. Cait chooses an SRS of 7 tiles. Let p-hat be the proportion of vowels in her sample.

Is the 10% condition met in this case?

• Yes.

• No.

• Not enough info to determine.

In the game of Scrabble, each player begins by drawing 7 tiles from a bag containing 100 tiles. There are 42 vowel, 56 consonants, and 2 blank tiles in the bag. Cait chooses an SRS of 7 tiles. Let p-hat be the proportion of vowels in her sample.

Is the Law of Large Counts met in this example?

• Yes.

• No.

• Not enough info to determine.

In the game of Scrabble, each player begins by drawing 7 tiles from a bag containing 100 tiles. There are 42 vowel, 56 consonants, and 2 blank tiles in the bag. Cait chooses an SRS of 7 tiles. Let p-hat be the proportion of vowels in her sample.

Cait only has 1 vowel of the 7 randomly selected tiles. She wants to know what the likelihood of this occurring. Are all conditions met for her to do this?

• No, the 10% condition is not met so we cannot calculate the standard deviation.

• No, the large counts condition is not met so we cannot assume this is approximately Normally distributed.

• Yes! Both the 10% condition and the Large Counts conditions were both met.

• There is not enough information to calculate this.

The Gallup Poll asked a random sample of 1785 adults whether they attended church during the past week.  Let p-hat be the proportion of people in the sample who attended church.  A newspaper report claims that 40% of all U.S. adults went to church last week.  Suppose this claim is true. 
What is the mean of the sampling distribution of p-hat?

• 0.4
• 0.44
• 0.56
• 0.6

The Gallup Poll asked a random sample of 1785 adults whether they attended church during the past week. Let p-hat be the proportion of people in the sample who attended church. A newspaper report claims that 40% of all U.S. adults went to church last week. Suppose this claim is true.

Calculate the standard deviation of the sampling distribution. (Check to see if the 10% condition is met first)

• 0.0116

• 0.0177

• 0.0181

• 0.0119

The Gallup Poll asked a random sample of 1785 adults whether they attended church during the past week. Let p-hat be the proportion of people in the sample who attended church. A newspaper report claims that 40% of all U.S. adults went to church last week. Suppose this claim is true.

Is the sampling distribution approximately Normal? (Check to see if the Large Counts condition is met).

• Yes.

• No.

The Gallup Poll asked a random sample of 1785 adults whether they attended church during the past week.  Let p-hat be the proportion of people in the sample who attended church.  A newspaper report claims that 40% of all U.S. adults went to church last week.  Suppose this claim is true. 
Of the poll respondents, 44% said they did attend church last week.  Find the probability of obtaining a sample of 1785 adults in which 44% or more say they attended church last week if the newspaper's claim is true. 

• 99%
• 4.4%
• 0.028 %
• Conditions were not met, so you cannot calculate this.