What value am I supposed to plug in for x?

[altitus]

Question -
The producers of a new toothpaste claim that it prevents more cavities than other brands of toothpaste. In other words, those who use the new toothpaste should have fewer cavities than other brands. Researchers sought to see if the new toothpaste had significantly fewer cavities than other brands. A random sample of 60 people uses the new toothpaste for six months. The mean number of cavities at their next checkup is 1.5. In the general population, the mean number of cavities at a six-month checkup is 1.73. The standard deviation is 1.12.

Decide whether to use a z test or a t test, and then find the z obt or the t obt.

I determined that the z test is needed for this problem. The options for answers are:

a. -1.675
b. +1.5
c. -1.643
d. + 2.643

I tried plugging in 60 for the x value in the equation for a z score, and none of the answers I come up with come anywhere close to the options for answers given in the multiple choice. If there's someone who can help a little, I'd greatly appreciate it.

 

[Deleted member 4993]

Question -
The producers of a new toothpaste claim that it prevents more cavities than other brands of toothpaste. In other words, those who use the new toothpaste should have fewer cavities than other brands. Researchers sought to see if the new toothpaste had significantly fewer cavities than other brands. A random sample of 60 people uses the new toothpaste for six months. The mean number of cavities at their next checkup is 1.5. In the general population, the mean number of cavities at a six-month checkup is 1.73. The standard deviation is 1.12.

Decide whether to use a z test or a t test, and then find the z obt or the t obt.

I determined that the z test is needed for this problem. The options for answers are:

a. -1.675
b. +1.5
c. -1.643
d. + 2.643

I tried plugging in 60 for the x value in the equation for a z score, and none of the answers I come up with come anywhere close to the options for answers given in the multiple choice. If there's someone who can help a little, I'd greatly appreciate it.

Please share your work (including your answers) so that we can know where to begin to help you.

 

[altitus]

Please share your work (including your answers) so that we can know where to begin to help you.

Ok. I attempted to use 60 as the value for X. that means that z=60-1.5/1.12. For that equation, I got approximately 59. I also tried 1.73-1.5/1.12 and got 0.366. I have tried using the values in the problem a few different ways, but never come up with numbers that resemble those given as options. I'm not sure where I'm going wrong. In my textbook, it uses an individual score in place of X in the examples, but this doesn't seem appropriate for this problem, because I don't have an individual score given that I could plug in.

 

[Dr.Peterson]

Ok. I attempted to use 60 as the value for X. that means that z=60-1.5/1.12. For that equation, I got approximately 59. I also tried 1.73-1.5/1.12 and got 0.366. I have tried using the values in the problem a few different ways, but never come up with numbers that resemble those given as options. I'm not sure where I'm going wrong. In my textbook, it uses an individual score in place of X in the examples, but this doesn't seem appropriate for this problem, because I don't have an individual score given that I could plug in.

But 60 is the sample size, which would usually be called n.

The variable x represents a value of the random variable, in this case the number of cavities; 1.73 makes a lot more sense, but that is the hypothesized mean, not the mean for the sample. Have you stated the hypotheses for the test, which helps to see which number is what?

Also the formula you are using is not appropriate to a sample. What is the formula you were given for z_obt?

Do you have an example of applying this test, so you can see how the various numbers are used?

 

[altitus]

But 60 is the sample size, which would usually be called n.

The variable x represents a value of the random variable, in this case the number of cavities; 1.73 makes a lot more sense, but that is the hypothesized mean, not the mean for the sample. Have you stated the hypotheses for the test, which helps to see which number is what?

Also the formula you are using is not appropriate to a sample. What is the formula you were given for z_obt?

Do you have an example of applying this test, so you can see how the various numbers are used?

Hi there. My apologies for the late response. I'm still working on this problem and and still confused. I've been trying a few different ways of solving the problem. The formula I was given for the z obt was z = x bar minus mu divided by small sigma with another x bar right next to small sigma. I'm sorry I don't know how to insert the symbols yet, either.

From what I understand, x bar is the general population mean, which is 1.73 minus mu, which is the sample mean of 1.5
sigma is supposed to be 1.12 for this problem, and if that's being multiplied by the population mean, 1.73, that still doesn't give me the answer that is offered in the multiple choice. I think I always came up with a number that was between negative and positive one, and that was it.

 

[Dr.Peterson]

The formula I was given for the z obt was z = x bar minus mu divided by small sigma with another x bar right next to small sigma. I'm sorry I don't know how to insert the symbols yet, either.

From what I understand, x bar is the general population mean, which is 1.73 minus mu, which is the sample mean of 1.5
sigma is supposed to be 1.12 for this problem, and if that's being multiplied by the population mean, 1.73, that still doesn't give me the answer that is offered in the multiple choice. I think I always came up with a number that was between negative and positive one, and that was it.

Your formula is: [MATH]z_{obt}=\frac{\bar{x}-\mu}{\sigma_{\bar{x}}}[/MATH], right? (No extra charge for the formatting.)

No, [MATH]\mu[/MATH] always represents a population mean, which in this case is what we want to show this new population (who use the new toothpaste) differs from; [MATH]\bar{x}[/MATH] always represents a sample mean. So you have those reversed.

Yes, [MATH]\sigma[/MATH] represents the population standard deviation, which we are assuming to be still valid. But do you have a formula for [MATH]\sigma_{\bar{x}}[/MATH], which is the standard deviation of the distribution of sample means? There should be a [MATH]\sqrt{n}[/MATH] in there somewhere ...

Looking for a reference to give you, in case your textbook somehow failed to define it, I find that many sources don't use that symbol. But here is one that does.

Now, if I recall correctly, I didn't get one of their choices, either.