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lina2011 [118]
2 years ago
8

a) The mean age of graduate students at a University is at most 31 y ears with a standard deviation of two years. A random sampl

e of 15 graduate students is taken. The sample mean is 32 years and the sample standard deviation is three years. Are the data significant at the 1% level? The p-value is 0.0264. State the null and alternative hypotheses and interpret the p-value. Write information given with correct symbols. Hypothesis interpret the p-value. b) A bottle of water is labeled as containing 16 fluid ounces of water. You believe it is less than that. What type of test would you use? c) Assume the null hypothesis states that the mean is at most 12. Is this a left-tailed, right-tailed, or two-tailed test? d) What should you do if α = p-value?
Mathematics
1 answer:
kari74 [83]2 years ago
3 0

Answer:

A.)

H0: μ ≤ 31

H1: μ > 31

B.)

H0: μ ≥ 16

H1: μ < 16

C.)

Right tailed test

D.)

If Pvalue is less than or equal to α ; we reject the Null

Step-by-step explanation:

The significance level , α = 0.01

The Pvalue = 0.0264

The decision region :

Reject the null if :

Pvalue < α

0.0264 > 0.01

Since Pvalue is greater than α ; then, we fail to reject the Null ;

Then there is no significant evidence that the mean graduate age is more Than 31.

B.)

H0: μ ≥ 16

H1: μ < 16

Null Fluid contains 16

Alternative hypothesis, fluid contains less than 16

One sample t - test

C.)

Null hypothesis :

H0 : μ ≤ 12

. The direction of the sign in the alternative hypothesis signifies the type of test or tht opposite direction of the sign in the null hypothesis.

Hence, this is a right tailed test ; Alternative hypothesis, H1 : μ > 12

d.)

If Pvalue is less than or equal to α ; we reject the Null.

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Suppose I ask you to pick any four cards at random from a deck of 52, without replacement, and bet you one dollar that at least
Tatiana [17]

Answer:

a) No, because you have only 33.8% of chances of winning the bet.

b) No, because you have only 44.7% of chances of winning the bet.

Step-by-step explanation:

a) Of the total amount of cards (n=52 cards) there are 12 face cards (3 face cards: Jack, Queen, or King for everyone of the 4 suits: clubs, diamonds, hearts and spades).

The probabiility of losing this bet is the sum of:

- The probability of having a face card in the first turn

- The probability of having a face card in the second turn, having a non-face card in the first turn.

- The probability of having a face card in the third turn, having a non-face card in the previous turns.

- The probability of having a face card in the fourth turn, having a non-face card in the previous turns.

<u><em>1) The probability of having a face card in the first turn</em></u>

In this case, the chances are 12 in 52:

P_1=P(face\, card)=12/52=0.231

<u><em>2) The probability of having a face card in the second turn, having a non-face card in the first turn.</em></u>

In this case, first we have to get a non-face card (there are 40 in the dech of 52), and then, with the rest of the cards (there are 51 left now), getting a face card:

P_2=P(non\,face\,card)*P(face\,card)=(40/52)*(12/51)=0.769*0.235=0.181

<u><em>3) The probability of having a face card in the third turn, having a non-face card in the first and second turn.</em></u>

In this case, first we have to get two consecutive non-face card, and then, with the rest of the cards, getting a face card:

P_3=(40/52)*(39/51)*(12/50)\\\\P_3=0.769*0.765*0.240=0.141

<u><em>4) The probability of having a face card in the fourth turn, having a non-face card in the previous turns.</em></u>

In this case, first we have to get three consecutive non-face card, and then, with the rest of the cards, getting a face card:

P_4=(40/52)*(39/51)*(38/50)*(12/49)\\\\P_4=0.769*0.765*0.76*0.245=0.109

With these four probabilities we can calculate the probability of losing this bet:

P=P_1+P_2+P_3+P_4=0.231+0.181+0.141+0.109=0.662

The probability of losing is 66.2%, which is the same as saying you have (1-0.662)=0.338 or 33.8% of winning chances. Losing is more probable than winning, so you should not take the bet.

b) If the bet involves 3 cards, the only difference with a) is that there is no probability of getting the face card in the fourth turn.

We can calculate the probability of losing as the sum of the first probabilities already calculated:

P=P_1+P_2+P_3=0.231+0.181+0.141=0.553

There is 55.3% of losing (or 44.7% of winning), so it is still not convenient to bet.

5 0
3 years ago
Estimate the answear by rounding each number to its greatest place: 199 x 91
Nataly [62]
I estimated the answer to be 18,000

Without estimation the answer would be 18,109
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3 years ago
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viktelen [127]
Haha wring subject but convergent
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Solve the equation.<br><br> –9x + 1 = –x + 17
VikaD [51]

Answer:

-9x+1 = -x +17

-8x = 16

x = -2

Step-by-step explanation:

8 0
3 years ago
5/12+(BLANK)=1/2 HEEEEEEEEEELLLLLLLLPPPP MEEEEEEEEEE
Flauer [41]

Answer:1/12


Step-by-step explanation:

5/12 + 1/12 = 6/12. When u simplify it it equals 1/2


8 0
3 years ago
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