![kdenormandie3122](/avatars/5551.jpg)
kdenormandie3122
20.05.2020 •
Mathematics
Sunspots have been observed for many centuries. Records of sunspots from ancient Persian and Chinese astronomers go back thousands of years. Some archaeologists think sunspot activity may somehow be related to prolonged periods of drought in the southwestern United States. Let x be a random variable representing the average number of sunspots observed in a 4-week period. In a random sample of 40 such periods from Spanish colonial times, the sample mean is x¯ = 47.0. Previous studies of sunspot activity during this period indicate that σ = 35. It is thought that for thousands of years, the mean number of sunspots per 4-week period was about µ = 41. Sunspot activity above this level may (or may not) be linked to gradual climate change. Do the data indicate that the mean sunspot activity during the Spanish colonial period was higher than 41? Use α = 0.05. (a) State the appropriate null and alternate hypothesis. (b) Compute the value of test statistic. (c) Using P-value method, state a conclusion.
Solved
Show answers
More tips
- F Family and Home How to Raise a Genius? Discover the Secrets Here...
- F Food and Cooking How to Properly Cook Buckwheat?...
- H Health and Medicine How to Tan in a Tanning Bed? Tips and Recommendations...
- S Style and Beauty How to Sew a Balloon Skirt: Detailed Tutorial and Tips on Choosing the Right Fabric...
- P Philosophy Personal attitude towards Confession: how to prepare and undergo the procedure correctly?...
- F Food and Cooking How to Make Cottage Cheese at Home: Simple and Quick Recipe with Step By Step Instructions...
- H Health and Medicine Which Water Are You Drinking? Is it Worth Buying Bottled Water?...
- H Health and Medicine What Makes a Man a Man?...
- H Health and Medicine What to Take with You to the Maternity Hospital?...
- F Food and Cooking What Foods Can Nursing Moms Eat?...
Answers on questions: Mathematics
- M Mathematics A recipe calls for 21 oz of flour for every 5 oz of milk. If you use 25 oz of milk, how much flour should you use?...
- M Mathematics Need help please i’m struggling to solve...
- M Mathematics Find the value of in the triangle shown below. 12...
- M Mathematics Find the perimeter of the triangle...
- M Mathematics What is the gcf of 12xy^2z and 8x^2y...
- M Mathematics Is this a transversal, parallel, perpendicular....
- M Mathematics What number lies between -2 and 3...
- M Mathematics If this correct too? Sorry if I ask again, I feel kinda insecure....
- M Mathematics Tania has already saved $25.75. She needs at least $53.88 to buy a set of headphones. Write and solve an inequality that shows how much more she needs to earn to...
- M Mathematics Joey has 2 friends that can eat the same amount as him. If they decided to order all SMALL pizzas, how many SMALL pizzas would they have to order? Explain how you...
Ответ:
(a) Null Hypothesis,
:
41
Alternate Hypothesis,
:
> 41
(b) The value of z test statistics is 1.08.
(c) We conclude that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41.
Step-by-step explanation:
We are given that in a random sample of 40 such periods from Spanish colonial times, the sample mean is x¯ = 47.0. Previous studies of sunspot activity during this period indicate that σ = 35.
It is thought that for thousands of years, the mean number of sunspots per 4-week period was about µ = 41.
Let
= mean sunspot activity during the Spanish colonial period.
(a) Null Hypothesis,
: ![\mu](/tpl/images/0657/3203/0746d.png)
41 {means that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41}
Alternate Hypothesis,
:
> 41 {means that the mean sunspot activity during the Spanish colonial period was higher than 41}
The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;
T.S. =
~ N(0,1)
where,
= sample mean = 47
σ = population standard deviation = 35
n = sample of periods from Spanish colonial times = 40
So, the test statistics =![\frac{47-41}{\frac{35}{\sqrt{40} } }](/tpl/images/0657/3203/431da.png)
= 1.08
(b) The value of z test statistics is 1.08.
(c) Now, the P-value of the test statistics is given by;
P-value = P(Z > 1.08) = 1 - P(Z < 1.08)
= 1 - 0.8599 = 0.1401
Since, the P-value of the test statistics is higher than the level of significance as 0.1401 > 0.05, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41.
Ответ: