Question

A new cream that advertises that it can reduce wrinkles and improve skin was subject to...

A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 42 women over the age of 50 used the new cream for 6 months. Of those 42 women, 36 of them reported skin improvement(as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 50% of women over the age of 50? Test using α=0.05.

(a) Test statistic: z=

(b) Critical Value: z∗=

(c) The final conclusion is A. There is not sufficient evidence to reject the null hypothesis that p=0.5. That is, there is not sufficient evidence to reject that the cream can improve the skin of more than 50% of women over 50. B. We can reject the null hypothesis that p=0.5 and accept that p>0.5. That is, the cream can improve the skin of more than 50% of women over 50.

Homework Answers

Answer #1

n = 42, x = 36

p̄ = x/n = 0.8571

α = 0.05

Null and Alternative hypothesis:

Ho : p = 0.5

H1 : p > 0.5

a) Test statistic:

z = (p̄ -p)/√(p*(1-p)/n) = (0.8571 - 0.5)/√(0.5 * 0.5/42) = 4.6285

b) Critical value :

Right tailed critical value, z crit = ABS(NORM.S.INV(0.05)) = 1.645

c) Decision:

z = 4.6285 > 1.645, Reject the null hypothesis

Conclusion:

B. We can reject the null hypothesis that p=0.5 and accept that p>0.5. That is, the cream can improve the skin of more than 50% of women over 50.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A new cream that advertises that it can reduce wrinkles and improve skin was subject to...
A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 64 women over the age of 50 used the new cream for 6 months. Of those 64 women, 33 of them reported skin improvement(as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 50% of women over the age of 50? Test using α=0.05 test statistics z= rejection region z>...
A new cream that advertises that it can reduce wrinkles and improve skin was subject to...
A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 42 women over the age of 50 used the new cream for 6 months. Of those 42 women, 30 of them reported skin improvement(as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 40% of women over the age of 50? Test using α=0.05. (a) Test statistic: z= (b) Critical...
A new cream that advertises that it can reduce wrinkles and improve skin was subject to...
A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 54 women over the age of 50 used the new cream for 6 months. Of those 54 women, 42 of them reported skin improvement(as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 40% of women over the age of 50? Test using α=0.05. (a) Test statistic: z= (b) Critical...
1. A new cream that advertises that it can reduce wrinkles and improve skin was subject...
1. A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 65 women over the age of 50 used the new cream for 6 months. Of those 65 women, 34 of them reported skin improvement(as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 60% of women over the age of 50? Test using α=0.05 (a) Test statistic: z= (b)...
A new cream that advertises that it can reduce wrinkles and improve skin was subject to...
A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 67 women over the age of 50 used the new cream for 6 months. Of those 67 women, 40 of them reported skin improvement(as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 60% of women over the age of 50? Test using ?=0.01 (a) Test statistic: ?= (b) Critical...
A new cream that advertises that it can reduce wrinkles and improve skin was subject to...
A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 40 women over the age of 50 used the new cream for 6 months. Of those 40 women, 30 of them reported skin improvement(as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 50% of women over the age of 50? Test using α=0.01. (a) Test statistic: z= (b) Critical...
A new cream that advertises that it can reduce wrinkles and improve skin was subject to...
A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 63 women over the age of 50 used the new cream for 6 months. Of those 63 women, 30 of them reported skin improvement(as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 40% of women over the age of 50? Test using α=0.05. (a) p-value =
(1 point) A new cream that advertises that it can reduce wrinkles and improve skin was...
(1 point) A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 4646 women over the age of 50 used the new cream for 6 months. Of those 4646 women, 3333 of them reported skin improvement(as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 6060% of women over the age of 50? Test using α=0.05α=0.05. test statistics z= rejection...
The paint used to make lines on roads must reflect enough light to be clearly visible...
The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let μ denote the true average reflectometer reading for a new type of paint under consideration. A test of H0: μ = 20 versus Ha: μ > 20 will be based on a random sample of size n from a normal population distribution. What conclusion is appropriate in each of the following situations? (Round your P-values to three decimal places.) (a)    z =...
"Durable press" cotton fabrics are treated to improve their recovery from wrinkles after washing. "Wrinkle recovery...
"Durable press" cotton fabrics are treated to improve their recovery from wrinkles after washing. "Wrinkle recovery angle" measures how well a fabric recovers from wrinkles. Higher is better. Here are data on the wrinkle recovery angle (in degrees) for a random sample of fabric specimens. Assume the populations are approximately normally distributed with unequal variances. A manufacturer believes that the mean wrinkle recovery angle for Hylite is better. A random sample of 25 Permafresh (group 1) and 20 Hylite (group...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT