Check whether the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Question

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Answer 1

Question

Chapter 15, Problem 62SE

To determine

Check whether the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Expert Solution & Answer

Answer to Problem 62SE

The conclusion is that the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Explanation of Solution

The hypotheses are given below:

Null hypothesis:

$H0:p=0.5$

Alternative hypothesis:

$Ha:p≠0.5$

Consider, the p-value is the probability of gourmet A’s rating exceeds gourmet B’s rating for a given meal.

From the given table, the number of gourmet A’s rating exceeds gourmet B’s rating for a given meal is 4. Hence, the test statistic (M) is 4.

The p-value is obtained below:

$p-value=2P(M≤4)=2[(170)0.50(1−0.5)17−0+⋅⋅⋅+(174)0.54(1−0.5)17−4]=2(0.02452)=0.04904$

Thus, the p-value is 0.04904.

Decision rule:

If $p-value≤α$ , then reject the null hypothesis.

Conclusion:

Here, the p-value is almost equal to the significance level 0.05.

From the rejection rule, the null hypothesis is rejected.

Hence, it can be concluded that the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

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Answer 2

Question

Chapter 15, Problem 62SE

To determine

Check whether the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Expert Solution & Answer

Answer to Problem 62SE

The conclusion is that the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Explanation of Solution

The hypotheses are given below:

Null hypothesis:

$H0:p=0.5$

Alternative hypothesis:

$Ha:p≠0.5$

Consider, the p-value is the probability of gourmet A’s rating exceeds gourmet B’s rating for a given meal.

From the given table, the number of gourmet A’s rating exceeds gourmet B’s rating for a given meal is 4. Hence, the test statistic (M) is 4.

The p-value is obtained below:

$p-value=2P(M≤4)=2[(170)0.50(1−0.5)17−0+⋅⋅⋅+(174)0.54(1−0.5)17−4]=2(0.02452)=0.04904$

Thus, the p-value is 0.04904.

Decision rule:

If $p-value≤α$ , then reject the null hypothesis.

Conclusion:

Here, the p-value is almost equal to the significance level 0.05.

From the rejection rule, the null hypothesis is rejected.

Hence, it can be concluded that the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 15, Problem 62SE

To determine

Check whether the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Expert Solution & Answer

Answer to Problem 62SE

The conclusion is that the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Explanation of Solution

The hypotheses are given below:

Null hypothesis:

$H0:p=0.5$

Alternative hypothesis:

$Ha:p≠0.5$

Consider, the p-value is the probability of gourmet A’s rating exceeds gourmet B’s rating for a given meal.

From the given table, the number of gourmet A’s rating exceeds gourmet B’s rating for a given meal is 4. Hence, the test statistic (M) is 4.

The p-value is obtained below:

$p-value=2P(M≤4)=2[(170)0.50(1−0.5)17−0+⋅⋅⋅+(174)0.54(1−0.5)17−4]=2(0.02452)=0.04904$

Thus, the p-value is 0.04904.

Decision rule:

If $p-value≤α$ , then reject the null hypothesis.

Conclusion:

Here, the p-value is almost equal to the significance level 0.05.

From the rejection rule, the null hypothesis is rejected.

Hence, it can be concluded that the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 15, Problem 62SE

To determine

Check whether the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Expert Solution & Answer

Answer to Problem 62SE

The conclusion is that the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Explanation of Solution

The hypotheses are given below:

Null hypothesis:

$H0:p=0.5$

Alternative hypothesis:

$Ha:p≠0.5$

Consider, the p-value is the probability of gourmet A’s rating exceeds gourmet B’s rating for a given meal.

From the given table, the number of gourmet A’s rating exceeds gourmet B’s rating for a given meal is 4. Hence, the test statistic (M) is 4.

The p-value is obtained below:

$p-value=2P(M≤4)=2[(170)0.50(1−0.5)17−0+⋅⋅⋅+(174)0.54(1−0.5)17−4]=2(0.02452)=0.04904$

Thus, the p-value is 0.04904.

Decision rule:

If $p-value≤α$ , then reject the null hypothesis.

Conclusion:

Here, the p-value is almost equal to the significance level 0.05.

From the rejection rule, the null hypothesis is rejected.

Hence, it can be concluded that the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 15, Problem 62SE

To determine

Check whether the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Expert Solution & Answer

Answer to Problem 62SE

The conclusion is that the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Explanation of Solution

The hypotheses are given below:

Null hypothesis:

$H0:p=0.5$

Alternative hypothesis:

$Ha:p≠0.5$

Consider, the p-value is the probability of gourmet A’s rating exceeds gourmet B’s rating for a given meal.

From the given table, the number of gourmet A’s rating exceeds gourmet B’s rating for a given meal is 4. Hence, the test statistic (M) is 4.

The p-value is obtained below:

$p-value=2P(M≤4)=2[(170)0.50(1−0.5)17−0+⋅⋅⋅+(174)0.54(1−0.5)17−4]=2(0.02452)=0.04904$

Thus, the p-value is 0.04904.

Decision rule:

If $p-value≤α$ , then reject the null hypothesis.

Conclusion:

Here, the p-value is almost equal to the significance level 0.05.

From the rejection rule, the null hypothesis is rejected.

Hence, it can be concluded that the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Answer 6

Chapter 15, Problem 62SE

To determine

Check whether the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Expert Solution & Answer

Answer to Problem 62SE

The conclusion is that the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Explanation of Solution

The hypotheses are given below:

Null hypothesis:

$H0:p=0.5$

Alternative hypothesis:

$Ha:p≠0.5$

Consider, the p-value is the probability of gourmet A’s rating exceeds gourmet B’s rating for a given meal.

From the given table, the number of gourmet A’s rating exceeds gourmet B’s rating for a given meal is 4. Hence, the test statistic (M) is 4.

The p-value is obtained below:

$p-value=2P(M≤4)=2[(170)0.50(1−0.5)17−0+⋅⋅⋅+(174)0.54(1−0.5)17−4]=2(0.02452)=0.04904$

Thus, the p-value is 0.04904.

Decision rule:

If $p-value≤α$ , then reject the null hypothesis.

Conclusion:

Here, the p-value is almost equal to the significance level 0.05.

From the rejection rule, the null hypothesis is rejected.

Hence, it can be concluded that the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Answer 7

Chapter 15, Problem 62SE

To determine

Check whether the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Answer 8

Expert Solution & Answer

Answer to Problem 62SE

The conclusion is that the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

The hypotheses are given below:

Null hypothesis:

$H0:p=0.5$

Alternative hypothesis:

$Ha:p≠0.5$

Consider, the p-value is the probability of gourmet A’s rating exceeds gourmet B’s rating for a given meal.

From the given table, the number of gourmet A’s rating exceeds gourmet B’s rating for a given meal is 4. Hence, the test statistic (M) is 4.

The p-value is obtained below:

$p-value=2P(M≤4)=2[(170)0.50(1−0.5)17−0+⋅⋅⋅+(174)0.54(1−0.5)17−4]=2(0.02452)=0.04904$

Thus, the p-value is 0.04904.

Decision rule:

If $p-value≤α$ , then reject the null hypothesis.

Conclusion:

Here, the p-value is almost equal to the significance level 0.05.

From the rejection rule, the null hypothesis is rejected.

Hence, it can be concluded that the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Answer 12

Ch. 15.3 - What significance levels between = .01 and = .15...Ch. 15.3 - Prob. 2E Ch. 15.3 - Clinical data concerning the effectiveness of two...Ch. 15.3 - Prob. 4E Ch. 15.3 - New food products are frequently subjected to...Ch. 15.3 - On clear, cold nights in the central Florida...Ch. 15.3 - A psychological experiment was conducted to...Ch. 15.3 - Refer to Exercise 12.15. Using the sign test, do...Ch. 15.3 - Prob. 9E Ch. 15.4 - The accompanying table gives the scores of a group...

Check whether the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

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Check whether the data provide sufficient evidence to indicate that one of gourmets tends to give higher ratings than the other.

Answer to Problem 62SE

Explanation of Solution

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