Question

Suppose that over the past 30 years during any given week of the major-league season, an average of µ = 12 players are hit by wild pitches. Assume that the distribution is normal with a standard deviation of σ =3. For a sample of n = 4 weeks, in which the daily temperature was extremely hot, the weekly average of hit-by- pitch players was M = 15.5.

Are players more likely to get hit by pitches during hot weeks? Use a one-tailed test with α = .05.

A) The null hypotheses in words is:

Group of answer choices

The number of hit-by-pitch players during hot weather remains the same

The number of hit-by-pitch players during hot weather significantly changes

There is a significant increase in the number of hit-by-pitch players during hot weather.

There is not a significant increase in the number of hit-by-pitch players during hot weather.

B)

The alternative hypothesis in symbols is:

Group of answer choices

H1: µ = 12

H1: µ ≠ 12

H1: µ > 12

H1: µ ≤ 12

H1: M ≤ 12

H1: M >12

H1: M ≠ 12

H1: M = 12

C)

The critical z value is

If it is a decimal number that is less than one, please include the 0 before the decimal point. If it is a decimal number with two or more than two places, leave only two decimal places after the decimal point. Please do not round. Finally, it is is a negative number, please do not forget to put the minus sign in front of it.

D)

The z-score statistic is:

If it is a decimal number that is less than one, please include the 0 before the decimal point. If it is a decimal number with two or more than two places, leave only two decimal places after the decimal point. Please do not round. Finally, it is is a negative number, please do not forget to put the minus sign in front of it.

E)

Your decision is

Group of answer choices

Reject the null hypothesis and conclude that that there is a significant increase in the number of hit-by-pitch players during hot weather

Reject the null hypothesis and conclude that that there is not a significant increase in the number of hit-by-pitch players during hot weather

Fail to reject the null hypothesis and conclude that that there is a significant increase in the number of hit-by-pitch players during hot weather

Fail to reject the null hypothesis and conclude that that there is not a significant increase in the number of hit-by-pitch players during hot weather

G)

Compute Cohen’s d to estimate the size of the effect.

Cohen's d is:

If it is a decimal number that is less than one, please include the 0 before the decimal point. If it is a decimal number with two or more than two places, leave only two decimal places after the decimal point. Please do not round.

H) Report the results in APA

Answer 1

Given : Sample size=n=4

Sample mean=M=15.5

Population standard deviation=

Population mean=

Significance level=

A)

The null hypotheses in words is:

There is a significant increase in the number of hit-by-pitch players during hot weather.

B)

The alternative hypothesis in symbols is:

H1: µ > 12

C) The critical z value is ,

; from the normal probability integral table

D) The z-score statistic is,

E) Decision : Here ,

Therefore ,

Reject the null hypothesis and conclude that that there is a significant increase in the number of hit-by-pitch players during hot weather.

G) The Cohen’s d to estimate the size of the effect is,

Cohan's d

H) Here , the Cohan's d of 1 suggest that the sample mean and population mean differ by one standrad deviation of the data.