Question

Hypothesis Testing

For 1-3 below simply set up the Null (Ho) and Alternative (H1) Hypothesis.

1/ Test the claim that less than 10% of households own a boat.

2/ Test the claim that the mean body weight of college students is greater than 160 lbs.

3/ Test the claim that the majority of people prefer iphones.

4/ For 4 and 5 below, perform the hypothesis test. (a) Set up the null and alternative hypothesis (b) Calculate the test statistic (c) Calculate the p-value (d) Reject or Fail to reject the Null (e) Make your conclusion.

5/ In a recent poll of 240 people, 67% indicated that the sale of firearms should be made stricter. Use a significance level of 0.05 to test the claim that the majority of people want stricter gun control laws.

6/ In a recent survey of 100 women, it was determined that the average age of marriage was 25 with a standard deviation of 3. Use a significance level of 0.05 to test the claim that the average of marriage for women is greater than 22 years of age (the average in 1980).

Answer 1

1)
H0 : p = 0.10
Ha : p < 0.10

2)
H0 : mu = 160
Ha : mu > 160

3)

5)

H0 : p = 0.5
Ha ; p > 0.5

Test statistics:

z = ( P - p) /sqrt(p*(1-p)/n)
= (0.67 - 0.5)/sqrt(0.5 * (1-0.5)/240)
= 5.2673

p value = 0.00001

we reject the null hypothesis
There is sufficient evidence to support the claim

6)
Hypothesis;
H0 : mu = 22
Ha : mu > 22

Test statistics:

z = ( x -mean)/(s/sqrt(n))
= ( 25 - 22)/(3/sqrt(100))
= 10

p value = 0.00001
we reject the null hypothesis
There is sufficient evidence to support the claim