Statistics and Probability Answers

A claim states that the mean income of families in a certain city is at least 18,500. What kind of hypothesis does the claim state?

Supposed three coins are tossed. Let X be the random variable representing the number of heads occur. Construct a table that shows the sample space and values of the random variable X

The principal of tala senior highschool claims that the students in his school have above average intellegence. A random sample of 30 students IQ scores have a mean score of 113. The mean population IQ is 100 with a standard deviation of 15. Is there an evidence to support his claim?

A normally distributed data has a mean of 200 and a standard deviation of 20.What are the two extreme scores, outside of which only 5% of the distribution are expected to fall?

A deck (52) of cards (clubs, diamonds, hearts and spades) is shuffled once. Estimate the probability of drawing a king and queen. Estimate the probability of drawing a 4 (four). Estimate the probability of drawing a card that is not a heart.

A survey of 1000 men ages 20 to 30 found that their heights were normally distributed, with a mean of 65 inches and a standard deviation of 2.5 inches. How many men have a height that is between 60 inches and 70 inches?

B. Sketch the normal curve and indicate the location of the rejection region.

1. z > 1.645
2. z < -2.33
3. z < -2.58 or z > 2.58

ACTIVITY 7. EXPLORING MORE ELEMENTS OF HYPOTHESIS TESTING

A. Complete the table showing the rejection regions for common values of 𝜶.

Alternative Hypothesis

𝜶 Left-Tailed Right-Tailed Two-Tailed 𝛼 = .10 1. ___________ z > 1.28 z < -1.645 or z > 1.645

𝛼 = .05 z < -1.645 2. _________ z < -1.96 or z > 1.96

𝛼 = 0.25 3. ___________ z > 1.96 4. _______________

𝛼 = .01 z < -2.33 5.__________ z < -2.58 or z > 2.58

B. State the null hypothesis and the alternative hypothesis in (a) words and in (b) symbols for each of the following:

1. The average age of Youtube users is 25.

(a) In words = Ho: __________ Ha: __________

(b) In symbols = Ho: __________ Ha: __________

2. The mean age of the grade 10 students enrolled in Marawi High School is 16 years old. (a) In words = Ho: __________ Ha: __________

(b) In symbols = Ho: __________ Ha: __________

3. A doctor wants to know if the average recovery time of a patient taking a particular medication is one month.

In words,

Ho: The average recovery time of a patient taking a particular medication is one month.

In symbols,

Ho: ____________

In words,

Ha: The average recovery time of a patient taking a particular medication is not one month.

In symbols,

Ha: μ ≠ 1 month