Question

A laboratory claims that the mean sodium level, ? , of a healthy adult is 141...

A laboratory claims that the mean sodium level, ? , of a healthy adult is 141 mEq per liter of blood. To test this claim, a random sample of 90 adult patients is evaluated. The mean sodium level for the sample is 140 mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is 14 mEq. Can we conclude, at the 0.05 level of significance, that the population mean adult sodium level differs from that claimed by the laboratory? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. (If necessary, consult a list of formulas.)

The null hypothesis: ?

The alternative hypothesis:?

The type of test statistic:?

The value of the test statistic: (Round to at least three decimal places.) ?

The p-value: (Round to at least three decimal places.)?

Can we conclude that the population mean adult sodium level differs from that claimed by the laboratory?

Homework Answers

Answer #1

Solution:

Null Hypothesis (Ho): = 141

Alternative Hypothesis (Ha): 141

Since population standard deviation is known, we use Z-test.

Test Statistics

Z = (141 - 140)/ (14/90)

Z = 0.678

Using Z-tables, the p-value is

P [Z 0.678] = P [Z < -0.678] + P [Z > 0.678]

= 0.249 + 0.249  

= 0.498

Since p-value is is greater than 0.05 level of significance, we fail to reject Ho.

Hence, we cannot conclude that the population mean adult sodium level differs from that claimed by the laboratory.

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 laboratory claims that the mean sodium level, μ , of a healthy adult is 141...
A laboratory claims that the mean sodium level, μ , of a healthy adult is 141 mEq per liter of blood. To test this claim, a random sample of 26 adult patients is evaluated. The mean sodium level for the sample is 144 mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is 11 mEq. Assume that the population is normally distributed. Can we conclude, at the 0.05 level of significance, that...
A laboratory claims that the mean sodium level, μ, of a healthy adult is 138 mEq...
A laboratory claims that the mean sodium level, μ, of a healthy adult is 138 mEq per liter of blood. To test this claim, a random sample of 43 adult patients is evaluated. The mean sodium level for the sample is 144 mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is 14 mEq. Assume that the population is normally distributed. Can we conclude, at the 0.05 level of significance, that the...
A laboratory claims that the mean sodium level, μ , of a healthy adult is 138...
A laboratory claims that the mean sodium level, μ , of a healthy adult is 138 mEq per liter of blood. To test this claim, a random sample of 50 adult patients is evaluated. The mean sodium level for the sample is 135 mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is 15 mEq. Can we conclude, at the 0.01 level of significance, that the population mean adult sodium level differs...
A manufacturer claims that the mean lifetime, u, of its light bulbs is 53 months. The...
A manufacturer claims that the mean lifetime, u, of its light bulbs is 53 months. The standard deviation of these lifetimes is 6 months. Ninety bulbs are selected at random, and their mean lifetime is found to be 52 months. Can we conclude, at the 0.05 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 53 months? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at...
A laboratory in Washington is interested in finding the mean chloride level for a healthy resident...
A laboratory in Washington is interested in finding the mean chloride level for a healthy resident in the state. A random sample of 70 healthy residents has a mean chloride level of 102 mEq/L. If it is known that the chloride levels in healthy individuals residing in Washington have a standard deviation of 42 mEq/L, find a 95% confidence interval for the true mean chloride level of all healthy Washington residents. Then complete the table below. Carry your intermediate computations...
A leasing firm claims that the mean number of miles driven annually, μ , in its...
A leasing firm claims that the mean number of miles driven annually, μ , in its leased cars is less than 12620 miles. A random sample of 30 cars leased from this firm had a mean of 11399 annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is 2660 miles. Assume that the population is normally distributed. Is there support for the firm's claim at the 0.05...
One urban affairs sociologist claims that the proportion, p , of adult residents of a particular...
One urban affairs sociologist claims that the proportion, p , of adult residents of a particular city who have been victimized by a criminal is at least 55% . A random sample of 245 adult residents of this city were questioned, and it was found that 119 of them had been victimized by a criminal. Based on these data, can we reject the sociologist's claim at the 0.05 level of significance? Perform a one-tailed test. Then fill in the table...
A college professor claims that the entering class this year appears to be smarter than entering...
A college professor claims that the entering class this year appears to be smarter than entering classes from previous years. He tests a random sample of 10 of this year's entering students and finds that their mean IQ score is 121 , with standard deviation of 14 . The college records indicate that the mean IQ score for entering students from previous years is 111 . If we assume that the IQ scores of this year's entering class are normally...
A leasing firm claims that the mean number of miles driven annually, μ , in its...
A leasing firm claims that the mean number of miles driven annually, μ , in its leased cars is less than 13160 miles. A random sample of 19 cars leased from this firm had a mean of 12833 annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is 1980 miles. Assume that the population is normally distributed. Is there support for the firm's claim at the 0.1...
The amount of water consumed each day by a healthy adult follows a normal distribution with...
The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 1.44 liters. A health campaign promotes the consumption of at least 2.0 liters per day. A sample of 10 adults after the campaign shows the following consumption in liters: 1.80 1.94 1.70 1.50 1.64 1.40 1.64 1.70 1.66 1.54 At the 0.100 significance level, can we conclude that water consumption has increased? Calculate and interpret the p-value. State the null hypothesis...